Phed IIT CoOrdinate Geometry 21

PhED IIT WorksheetCo Ordinate geometry 2014 - 15

NAME OF CHAPTER NAME OF BOOK QUESTION NUMBER ANSWER QUES TYPE MARKS LEVEL

A 3x-4y+1=0 B 4x+3y-5=0 C 7x-y+4=0 D none of these

A (3,-1),(3,-6) B (3,1),(3,5) C (3,2),(3,6) D (3,1),(3,6)

A (16,-2) B (-16,2) C (16,2) D (-16,-2)

A 10 B 20 C 40 D none of these

A coordinates which are irrational Batleast one coordinate which

is irrationalC coordinates which are rational D

coordinates which are integers

A x=0 B x=-a C x=3a D x=-3a

A 4√2 B 5√2 C √2 D none of these


A has a fixed direction Balways passes through a

fixed pointC

always cuts intercepts on the

axes such that their sum is 0D

forms a triangle whose are is constant with

the axes

A 2 B 0 C 4 D 1

A (0,5) or (4,1) B (5,0) or (1,4) C (5,0) or (4,1) D (0,5) or (1,4)

A rectangle B square C cyclic quad. D rhombus

A 1:2 B 3:4 C 2:1 D 4:3

A not concurrent B concurrent in(1,-1) C concurrent at (1,1) D none of these

A straight line B circle C a parabola D an ellipse

QUESTION / OPTIONS

11A MCQ3Straight Lines Dinesh KhattarGiven the system of straight line a(2x+y-3)+b(3x+2y-5)=0 the line of the system farthest from the point (4,-3) has the equation

D MCQ 1 1Straight Lines Dinesh Khattar 7A rectangle has two opposite vertices at the points (1,2) and (5,5) . If the other vertices lie on the line x=3, then the coordinates of the other vertices are

MCQ 1 1Straight Lines Dinesh Khattar 10The image of the point (-8,12) with respect to the line mirror 4x+7y+13=0 is

D

MCQ 1 1Straight Lines Dinesh Khattar 18The area of the region enclosed by 4|x|+5|y|=20 is

C

MCQ 1 1Straight Lines Dinesh Khattar 25

If two vertices of an equilateral triangle have integral co ordinates then the third vertex will have

B

MCQ 1 1Straight Lines Dinesh Khattar 32The base of a triangle lies along the line x=a and is of length a.The area of the triangle is a

2, if the vertex lies on the line

B,C

MCQ 1 1Straight Lines Dinesh Khattar 27The distance of the point (2,3) from the line 3x+2y=17 measured parallel to the line x-y=4 is

C

MCQ 1 1Straight Lines Dinesh Khattar 33If P and Q are two points on the line 4x+3y+30=0 such that OP=OQ =10 where O is the origin , then area of OPQ is

A

MCQ 1 1Straight Lines Dinesh Khattar 54The number of integer values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=mx+1 is also an integer is

A


If a,b,c are three terms of an AP then the line ax+by+c=0

B

MCQ 1 1Straight Lines Dinesh Khattar 60The diagonals of a parallelogram PQRS are along the lines x+3y=4 and 6x-2y=7.Then PQRS must be

D

MCQ 1 1Straight Lines Dinesh Khattar 59Two vertices of a triangle are(2,-1) and (3,2) and third vertex lies on the linex + y = 5. If the area of the triangle is 4 units and the third vertex is

B


A straight line through the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at points P and Q respectively.The point O divides the segment PQ in

the ratio B

MCQ 1 1Straight Lines Dinesh Khattar 87The straight line of the family x(a+b)+y(a-b)=2a(a and b are parameters) are

C

MCQ 1 1Straight Lines Dinesh Khattar 99A point moves so that it remains the third vertex of a right angled triangle,the ends of whose hypotenuse always remians as (a,0) and (b,0) traces out

B

[email protected] 98367 33221 1 / 7


NAME OF CHAPTER NAME OF BOOK QUESTION NUMBER ANSWER QUES TYPE MARKS LEVELQUESTION / OPTIONS

Given the system of straight line a(2x+y-3)+b(3x+2y-5)=0 the line of the system farthest from the point (4,-3) has the equation

A 29/5 B 5 C 6 D 5-Nov

A (1,√3/2) B (2/3,1/√3) C (2/3,√3/2) D (1,1/√3)

A lie on a straight line B lie on an ellipse C lie on a circle D ure vertices of a triangle

A (3x-1)2+(3y)

2=a

2-b

2 B (3x-1)2+(3y)

2=a

2+b

2 C (3x-1)2+(3y)

2=a

2+b

2 D (3x+1)2+(3y)

2=a

2-b

2

A 3x+2y=5 B 2x-3y=7 C 2x+3y=9 D 3x-2y=3

A(x/2)+(y/3)=-1 and

(x/-2)+(y/1)=-1B

(x/2)-(y/3)=-1 and

(x/-2)+(y/1)=-1C

(x/2)+(y/3)=1 and

(x/-2)+(y/1)=1D

(x/2)-(y/3)=1 and

(x/-2)+(y/1)=1

Aabove the x-axis at a distance

of(2/3) from itB

above the x-axis at a distance

of(3/2) from itC

below the x-axis at a distance

of(2/3) from itD

below the x-axis at a distance of(2/3) from

it

A 3x-4y+7=0 B 4x-3y+7=24 C 3x+4y=25 D x+y=7

A (-1,3) B (-3,-2) C (1,3) D (0,2)

A -4 B 1 C 2 D -2

A (√3/2)+y=0 B (x+√3y=0) C (√3x)+y=0 D x+(√3/2)y=0

Straight Lines A.Mitra - Subj 4 1.414, 225 Subjective 4 4

Straight Lines A.Mitra - Subj 8 5x+3y+32=0 Subjective 4 4

Straight Lines A.Mitra - Subj 11 (5,2) , (5,12) Subjective 4 4

Straight Lines A.Mitra - Subj 14 - (xv) x-3y=10 Subjective 4 4

Straight Lines A.Mitra - Subj 17 3x+y=0 Subjective 4 4

Straight Lines A.Mitra - Subj 16 3x+4y-4=0 Subjective 4 4

Straight Lines A.Mitra - Subj 18 Subjective 4 4

MCQ 1 1Straight Lines Dinesh Khattar 122If the line 2x+y=k passes through the point which divides the line segment joinig the points (1,1) and (2,4) in the ratio 3:2 then K equals :

C

1MCQ 1D2Straight Lines IIT - PREV YEARSThe incentere of the triangle with vertices (1,√3) ,(0,0) and (2,0) is

Straight Lines IIT - PREV YEARS 6If x1,x2,x3 and y1,y2,y3 are both in GP with the same common ratio then the points (x1,y1),(x2,y2),(x3,y3)

A MCQ 1 1

Straight Lines IIT - PREV YEARS 8Locus of a centroid of the triangle whose vertices are (a cos t , a sin t ) ,(b sin t ,-b cos t) and (1,0) where t is a parameter is

B MCQ 1 1

Straight Lines IIT - PREV YEARS 10Let A(2,-3) and B (-2,1) be the vertices of a triangle ABC.if the centroid of this triangle moves on the line 2x+3y=1,then locus of the vertex C is the line

C MCQ 1 1

Straight Lines IIT - PREV YEARS 11

The equation of the straight line passing through the point (4,3) and making intercepts on the coordinates axes whose sum -1 is

D MCQ 1 1


The line parallel to the x-axis and passing through the intersection of the lines ax+2by+3b=0 and bx-2ay-3a=0,where(a,b) not equal to (0,0) is

D MCQ 1 1

Straight Lines IIT - PREV YEARS 16A straight line through the point A(3,4) is such that its intercept between the axes is bisected at A. its equation is

C MCQ 1 1


Let A(h,k),B(1,1) and C(2,1) be the vertices of a right angled triangle with AC as its hypotenuse.If the area of the triangle is 1 square unit, then the set of

values which k can take is given by A MCQ 1 1

Straight Lines IIT - PREV YEARS 22The perpendicular bisector of the line segment joining P(1,4) and Q(k,3) has y intercept -4.then a possible values of k is

A MCQ 1 1

Straight Lines IIT - PREV YEARS 20Let P=(-1,0),Q=(0,0) and R=(3,3√3) be the three points.The equation of the bisector of the angle POR is

C MCQ 1 1

Find the polar coordinates of the point (-1,-1)

If the lines 2x+3ay-1=0 and 3x+4y+1=0 are mutually perpendicular to each other find the value of a

Find the locus of a point which forms a triangle of area 21 sq unit with the point (2,-7) and (-4,3)

The ends of a diagonal of a rectangle are (2,3) and (8,11).If its other diagonal is parallel to y-axis find the coordinate of its ends

The foot of the perpendicular from (0,0) on a line Is(1,-3).Find the equation of the line

Find the equation of the straight line which passes through the intersection of lines 2x-y+5=0 and 5x+3y-4=0 and is perpendicular to x-3y+21=0

Find the equation of the straight line which passes through the intersection of lines 2x+6y-1=0 and 4x-2y-9=0 and is parallel to 3x+4y=0




Given the system of straight line a(2x+y-3)+b(3x+2y-5)=0 the line of the system farthest from the point (4,-3) has the equationStraight Lines A.Mitra - Subj 30 (1,1) Subjective 4 4

Straight Lines A.Mitra - Subj 31 5 unit Subjective 4 4




Straight Lines A.Mitra - Subj 47 60 Subjective 4 4


A 10 units B 15 units C 5 units D none

A x+y=2√2 B x+y=2√2 C x+2y=√2 D x-2y=√2

A r<2 B r=2 C r>2 D 2<r<8

A circle B ellipse C parabola D hyperbola

A all values of P B all except one value of P C all except two values of P D exactly one value of p

A -85<m<-35 B -35<m<15 C 15<m<65 D 35<m<85

A 1 B 2 C 3 D 4

A x2+y

2+6x-16y+28=0 B x

2+y

2+6x-16y+28=0 C x

2+y

2+6x-16y+28=0 D x

2+y

2+6x-16y+28=0

A 0 B 1 C 3 D 4

A 38 B -38 C 42 D none of these

A (-3/2,1/2) B (3/2,1/2) C (-3/2,-1/2) D (-3/2,-1/2)

A 8x-12y+25=0 B 6x-8y-25=0 C 12x-8y+25=0 D none of these

A 16x+8y±25=0 B 16x+8y±25=0 C 8x+6y±25=0 D none of these

Circles Dinesh Khattar 27The locus of the centre of the circles which cut the circles x

2+y

2+4x-6y+9=0 abd x

2+y

2-4x+6y+4=0 orthogonally is

A MCQ 1 1

Circles Dinesh Khattar 31

Extremities of a diagonal of a rectangle are (0,0) and (4,3) . The equations of the tangents to the circumcircle of the rectangle whch are parallel to this

diagonal are B MCQ 1 1

Circles Dinesh Khattar 18If the circle x

2+y

2+6x+8y+a=0 bisects the circumference of the circle x

2+y

2+2x-6y-b=0

B MCQ 1 1

Circles Dinesh Khattar 22The coordinates of the middle point of the chord which the circle x2+y2+4x-2y-3=0 cuts off the line y=x+2

A MCQ 1 1

Circles Dinesh Khattar 3the equation of the circle which has a tangent 2x-y-1 =0 at (3,5) on it and with the centre on x+y=5 is

A MCQ 1 1

Circles Dinesh Khattar 13The number of common tangents to the circle x

2+y

2=4 and x

2+y

2-6x-8y-24=0 is

B MCQ 1 1

Circles IIT - PREV YEARS 13The circle x

2+y

2=4x+8y+5 intersects the line 3x-4y=m at two distinct points if

B MCQ 1 1

Circles Dinesh Khattar 1The number of common tangents to the circle x

2+y

2=4 and x

2+y

2-8x+12=0

C MCQ 1 1

Circles IIT - PREV YEARS 7A circle touches the X-axis and also touches the circle with centre at (0,3) and radius 2. The locus of the center of the circle is

C MCQ 1 1

Circles IIT - PREV YEARS 12If P and Q are points of intersection of the circles x

2+y

2+3x+7y+2p-5=0 and x

2+y

2+2x-p

2=0 then there is a circle passing through P,Q and (1,1) for

C MCQ 1 1

Circles IIT - PREV YEARS 2The equation of the tangent to the circle x

2+y

2+4x-4y+4=0 which makes equal intercepts on the positive coordinate axes is

B MCQ 1 1

Circles IIT - PREV YEARS 3If the two circles (x-1)

2+ (y-3)

2= r

2and x

2+y

2-8x+2y+8=0 intersect in two distinct points then

D MCQ 1 1

Circles IIT - PREV YEARS 1The greatest distance of the point p(10,7) from the circle x

2+y

2-4x-2y-20=0 is

C MCQ 1 1

(1,2) and (3,8) are a pair of opposite vertices of a square .Find the coordinates of the other two vertices and the equations of the side passing through

(1,2)

The equation of the perpendicular bisector of the line segment PQ is 8x+6y-29=0 P be a point (-1,2) finr the Q coordinate

If p and p' be the perpendicular from the origin upon the straight lines x sec A+y cosec A=b and x cos A - y sin A = a cos A, prove that 4p2+p'

2= a

2

Show that the straight line (b-c)x+(c-a)y+(a-b)=0 passes through a fixed point.Find the coordinates

Find the distance of the line 3x+y+4=0 from the point (2,5)measured parallel to the line 3x-4y+8=0

Prove that all points on the line 11x-3y+11=0 are equidistant from the lines 12x+5y+12=0 and 3x-4y+3=0

At what angle with the line x+y=4 a line , through the point (1,2) be drawn that the distance between the point of intersection of the lines and the point

(1,2) is √6/3 units





A 2x-3y+1=0 B 2x+3y+1=0 C 3x-2y+1=0 D none of these

A x+3y=0 B 3x-y=0 C x-3y=0 D x+y=0

A √5 B 2√5 C 3√5 D 4√5

A x2+y

2+x+y-8=0 B x

2+y

2+x+y-8=0 C x

2+y

2+x+y-8=0 D none of these

A x2+y

2-4x+8y+y=0 B x

2+4x+8y-4=0 C x

2-4x-8y+4=0 D none of these

A ∏/6 B ∏/4 C ∏/3 D ∏/2

A x2+y

2=9a2 B x

2+y

2=16a2 C x

2+y

2=4a2 D x

2+y

2=a2

A (1,1) B (-1,-1) C (-1,1) D (1,-1)

A (2+8/√5,1+4/√5) B (1+4/√5,2+8/√5) C (1+8/√5,2+4/√5) D none of these

A x2+y

2-4x-4y-8=0 B x

2-4x-8y+4=0 C x

2+y

2-4x-5y+6=0 D x

2-4x+4=0

A 10/3 B 3/5 C 6/5 D 5/3

A (3,-4) B (-3,4) C (-3,-4) D (3,4)

Circles A.Mitra - Subj 53 x2+y

2-4x-6y+4=0 Subjective 4 4


2-6x-6y+9=0 Subjective 4 4

Circles A.Mitra - Subj 60 none Subjective 4 4



2-5x+5y=0 Subjective 4 4



2-2x=0 Subjective 4 4

Circles A.Mitra - Subj 79 a2-2a(x+y)+2xy=0 Subjective 4 4

A x=-1 B x=1 C x=(-3/2) D x=3/2Parabola IIT - PREV YEARS 1

The equation of the directrix of the parabola y2+4y+4x+2=0 is

D MCQ 1 1

Find the equation of the circle which is concentric with the circle x2+y

2-4x-6y-5=0 and touches the line 4x+3y=2

Find the equation of the circle which touches both axes and the line 3x+4y=6

Prove that the circles x2+y

2+2ax+c=0 and x

2+y

2+2by+c=0 touch each other if 1/a

2+1/b

2=1/c

Show that the locus of the middle points of the chords of the circle x2+y

2=a

2which pass through the point (h,k) is x

2+y

2=hx+ky

Fint the eqn. of a circle that bisects the circumference of the circle x2+y

2+2y-3=0 and touches the line x-y=0

Twp rods of length a and b slide along the axes of co-ordinates in such a manner that their ends are cycloconic .Prove that the locus of the centre of the

circle passing through these ends is the curve 4(x2-y2)=a2-b2

Find the equations of the circle which passes through the origin and cut off equal chords √2 unit from the lines y=x and y=-x

Find the length of the common chord circles (x-a)2+y

2=a

2and x

2+(y-b)

2=b

2

Circles Dinesh Khattar 102The length of the diameter of the circle which touches the x-axis at the point (1,0) and passes through the point (2,3) is

B MCQ 1 1

Circles Dinesh Khattar 104The point diametrically opposite to the point P(1,0) on the circle x

2+y

2+2x+4y-3=0 is

C MCQ 1 1

Circles Dinesh Khattar 86The coordinates of the point of the circle x

2+y

2-2x-4y-11=0 farthest from the origin are

B MCQ 1 1

Circles Dinesh Khattar 89The locus of a centre of a circle which touches the x-axis and also the circle x

2+y

2-4x-4y=0 externally is

B MCQ 1 1

Circles Dinesh Khattar 64The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

C MCQ 1 1

Circles Dinesh Khattar 76The circle passing through three distinct points (1,t),(t,1) and (t,t) passing through the point

A MCQ 1 1

Circles Dinesh Khattar 53The locus of the centre of the circle which tousches the X-axis and also the circle x

2+y

2-4x-4y+4=0

C MCQ 1 1

Circles Dinesh Khattar 58The common chord of x

2+y

2-4x-4y=0 and x

2+y

2=16 subtends at the origin an angle equal to

D MCQ 1 1

Circles Dinesh Khattar 47If a circle passes through the points (1,0) , (5,0) and touches the y-axis at (0,h) then h =

A MCQ 1 1

Circles Dinesh Khattar 50The equation of the smallest circle passing through the intersection of the line x+y=1 and the circle x

2+y

2=9 is

B MCQ 1 1

Circles Dinesh Khattar 38The locus of the centre of the circles passing through the origin and cutting the circle x

2+y

2+6x-4y+2=0 orthogonally is

C MCQ 1 1

Circles Dinesh Khattar 413x+y=0 is a tangent to a circle with centre (2,-1) then the other tangent to the circlefrom origin is

C MCQ 1 1





A (-9/8),(9/2) B (2,-4) C (2,4) D (9/8),(9/2)

A (2,4) B (-2,0) C (-1,1) D (o,2)

A a=2c B |a|=2c C e D |a|=c

A x2/12 + y

2/16 =1 B x

2/16 + y

2/12 =1 C x

2/3+ y

2/4 =1 D x

2/4 + y

2/3 =1

A 3/5 B 1/2 C 4/5 D 1/√5

A x2+16y2=16 B x2+12y2=16 C x2+48y2=48 D x2+64y2=48

A 3x2+5y

2-15=0 B 5x

2+3y

2-32=0 C 3x

2+5y

2-32=0 D 5x

2+3y

2-48=0

A [x/(x1+x2)]+[y/(y1+y2)]=1 B [x/(x1-x2)]+[y/(y1-y2)]=1 C [y/(x1+x2)]+[x/(y1+y2)]=1 D [y/(x1-x2)]+[x/(y1-y2)]=1

A (-9/8),(9/2) B (2,-4) C (2,4) D (9/8),(9/2)

A (2,4) B (-2,0) C (-1,1) D (o,2)

A y2+4y+4x-8=0 B y2+4y-4x+8=0 C y2+4y-4x-8=0 D none of these

A 3 B 1/3 C 2 D 1/2

A 16/5 B 8/5 C 12/5 D none of these

A (4,-1) B (0,1) C (-4,1) D none of these

A m1+m1=0 B m1m2=-1 C m1m2=1 D none of these

A y2=-12(x-3) B y

2=12(x-3) C x

2=12(y-3) D x

2=-12(y-3)

Conics Section Dinesh Khattar 15The locus of a point whose sum of the distance from origin and the line x=2 is 4 units , is

C MCQ 1 1

Conics Section Dinesh Khattar 9

A ray of light is coming along the line which is parallel to y-axis and strikes a concave mirror whose intersection with xy-plane is a parabola (x-4)2=4(y+2)

.After reflection , the ray must pass through the point B MCQ 1 1

Conics Section Dinesh Khattar 10The parametric representations (3+t

2,3t-2) represents a parabola with

B MCQ 1 1

Conics Section Dinesh Khattar 3Two tangents are drawn from the point (-2,-1) to the parabola y

2=4x. If a is the angle between them then tan a =

A MCQ 1 1

Conics Section Dinesh Khattar 5The length of the latus rectum of the parabola 25[(x-2)

2+(y-4)

2]=(4x-3y+12)

2

B MCQ 1 1

Hyperbola IIT - PREV YEARS 7

The equation of the tangent of the parabola y2=8x is y=x+2.The point on this line from which the other tangent to the parabola is perpendicular to the

given tangent is B MCQ 1 1

Conics Section Dinesh Khattar 2Equation of the parabola whose vertex is (-3,-2) axis is horizontal and which passes through the point (1,2) is

C MCQ 1 1

Hyperbola IIT - PREV YEARS CH-17, 1The equation of the chord joining the two points (x1,y1) and (x2,y2) on rectangular hyperbola xy=c

2is

D MCQ 1 1

Hyperbola IIT - PREV YEARS 3A point on the parabola y

2=18x at which the ordinate increases at twice the rate of the abcissa is

D MCQ 1 1

Ellipse IIT - PREV YEARS 8

The ellipse x2+4y

2=4 is inscribed in a rectangle aligned with the coordinate axes,which in turn is inscribed in another ellipse that passes through the point

(4,0).Then the equation of the ellipse is A MCQ 1 1

Ellipse IIT - PREV YEARS 9Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3,1) and has eccentricity √(2/5) is

D MCQ 1 1

Ellipse IIT - PREV YEARS 1The equation of the ellipse whose foci are (±2,0) and eccentricity is (1/2) is

B MCQ 1 1

Ellipse IIT - PREV YEARS 6

In an ellipse the distance between its foci is 6 and minor axis is 8.Then the eccentricity is

A MCQ 1 1

Parabola IIT - PREV YEARS 7The equation of the tangent of the parabola y

2=8x is y=x+2.The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

B MCQ 1 1

Parabola IIT - PREV YEARS 10The two circles x

2+y

2=ax and x

2+y

2=c

2(c>0) touch each other if

D MCQ 1 1

Parabola IIT - PREV YEARS 3A point on the parabola Y

2=18x at which the ordinate increases at twice the rate of the abcissa is

D MCQ 1 1





A ellipse B hyperbola C parabola D none of these


A 2(y1)2=9 x1 B 2(x1)

2=9 y1 C 4(y1)

2=9 x1 D none of these

A ∏/4 B ∏/3 C 3∏/4 D 2∏/3

A 0 B 2 C 3 D 4

A |t|≤1 B |t|>1 C |t|<3 D none of these

A ∏/3 B ∏/4 C ∏/6 D ∏/2

A a parabola B an ellipse C a hyperbola D none of these

A √2/3 B 1/√3 C 1/√2 D 2/√5

A 30√5 B 25√2 C 152 D none of these

A hyperbolas B elllipses C parabolas D none of these

A 5/4 B 4/5 C 9/16 D 16/9

A 1 B 2 C 0 D 3

A x-y+1=0 B 3x+4y=25 C x+y-7=0 D none of these

A 9x2-8y

2+18x-9=0 B 9x

2-8y

2-18x+9=0 C 9x

2-8y

2-18x-9=0 D 9x

2-8y

2+18x+9=0

Parabola A.Mitra - Subj 83 (1,2) ;(0,2) Subjective 4 4

Parabola A.Mitra - Subj 86 y2=2ax Subjective 4 4

Parabola A.Mitra - Subj 88 (a/t2

, -2a/t) Subjective 4 4

Parabola A.Mitra - Subj 92 none Subjective 4 4

Find the focus , latus rectum, axis and the equation of the directrix of the parabola y2=4(y-x)

Find the locus of the middle points of all chords of the parabola y2=4ax which pass through the vertex.

If one end of a focal chord of the parabola y2=4ax be (at2,2at) find the co-ordinates of the other end.Show that the length of the chord is a(t+1/t)

2

The lengths of the two segments of any focal chord of any focal chord of the parabola y2=4ax are l and l' , prove that 1/l+1/l'=1/a

Conics Section Dinesh Khattar 84Equation of the straight line passing through the point (3,4) and farthest from the circle x

2+y

2+8x+6y+16=0 is

C MCQ 1 1

Conics Section Dinesh Khattar 86If x=9 is the chord of the contact of the hyperbola x

2-y

2=9 then the equation of the corresponding pair of tangents is

D MCQ 1 1

Conics Section Dinesh Khattar 77The eccentricity of the hyperbola 9x

2-16y

2+72x-32y-16=0 is

A MCQ 1 1

Conics Section Dinesh Khattar 78The number of tangents to the hyperbola x

2/4-y

2/3=1 through (4,1) is

B MCQ 1 1

Conics Section Dinesh Khattar 67The product of length of perpendicular drawn from the two foci to the tangent at any point on the ellipse 25x

2+4y

2=100 is

D MCQ 1 1

Conics Section Dinesh Khattar 74If e, e' be the eccentricities of two conics S=0 and S'=0 and if e

2+e'

2=3 then both S and S' can be

A MCQ 1 1

Conics Section Dinesh Khattar 70If a circle makes intercepts of length 5 and c on two perpendicular lines, then the locus of the centre of the circle is

C MCQ 1 1

Conics Section Dinesh Khattar 66If y=x and 3y+2x=0 are the equations of a pair of conjugate diameters of an ellipse then the eccentricity of the ellipse is

B MCQ 1 1

Conics Section Dinesh Khattar 48The line y=2t

2meets the ellipse x

2/9+y

2/4=1 in real points if

A MCQ 1 1

Conics Section Dinesh Khattar 52If the distance of a point on the ellipse x

2/6+y

2/2=1 from the centre is 2,then the eccentric angle is

B MCQ 1 1

Conics Section Dinesh Khattar 41Eccentric angle of a point on the ellipse X

2+3y2=6 at a distance 2 units from the centre of the ellipse

A,C MCQ 1 1

Conics Section Dinesh Khattar 44The number of real tangents that can be drawn to the ellipse 3x

2+5y

2=32 and 25x

2+9y

2=450 passing throufh (3,5) is

C MCQ 1 1

Conics Section Dinesh Khattar 29Maximum number of common normals of y

2=4ax and x

2=4by may be equal to

B MCQ 1 1

Conics Section Dinesh Khattar 37If two tangents drawn from the point (x1,y1) to the parabola y

2=4x be such that the slope of one tangent is double of the other, then

A MCQ 1 1

Conics Section Dinesh Khattar 22The conic represented by the equation √ax+√by=1 is

C MCQ 1 1




Given the system of straight line a(2x+y-3)+b(3x+2y-5)=0 the line of the system farthest from the point (4,-3) has the equationEllipse A.Mitra - Subj 99 x2/36+y

2/100=1 Subjective 4 4

Ellipse A.Mitra - Subj 101 ∏/4 Subjective 4 4

Ellipse A.Mitra - Subj 104(x-3)

2/36 +

(y-5)2/100 = 1

Subjective 4 4

Ellipse A.Mitra - Subj 108 1/√3 Subjective 4 4

Ellipse A.Mitra - Subj 114 none Subjective 4 4

Hyperbola A.Mitra - Subj 116 x2/16-y

2/20=1 Subjective 4 4

Hyperbola A.Mitra - Subj 120 3x2-y

2=3a

2 Subjective 4 4

Hyperbola A.Mitra - Subj 124 32x=9y Subjective 4 4

Find the equation of the hyperbola having vertices at (±4.0) and foci at (±6.0)

Find the equation of the hyperbola whose transverse axis is 2a and whose vertex bisects the distance between the centre and the focus.

Find the equation of the diameter of the hyperbola 16x2-9y

2=144 conjugate to x=2y

The foci of an ellipse are (0,±8) and eccentricity is 4/5 ; find the equation of the ellipse

Find the eccentric angle of a point on the ellipse x2+3y

2=6 at distance 2 unit from the center

Find the equation of the ellipse whose center is (1,2) directrix is 4x-29=0 and eccentricity is 4/5

If y=x and 2x+3y=0 are the equations of a pair of conjugate diameters of an ellipse then the eccentricity of the ellipse is

PQ and PR are two focal chords of an ellipse and the eccentric angles of P,Q,R are 2a,2b,2c respectively. Prove that tan a tan b tan c = cot a


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Phed IIT CoOrdinate Geometry 21