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JEECONCEPTSBOOSTER
CIRCLES
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1
CONCEPTFORJEE||ChapterCIRCLES
1.INTRODUCTION
1.Standardequationofcircle
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CONCEPTFORJEE||ChapterCIRCLES
2.SOMEPARTICULARCASESFOREQUATIONOFTHECIRCLE.
1.GeneralEquationofCircleWhenthecirclepassesthroughtheorigin.
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CONCEPTFORJEE||ChapterCIRCLES
2.SOMEPARTICULARCASESFOREQUATIONOFTHECIRCLE.
2.GeneralEquationofCircleWhenthecircletouchxaxisandyaxis.
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CONCEPTFORJEE||ChapterCIRCLES
2.SOMEPARTICULARCASESFOREQUATIONOFTHECIRCLE.
3.GeneralEquationofCircleWhenthecircletouchesboththeaxis.
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CONCEPTFORJEE||ChapterCIRCLES
3.SOMEPARTICULARCASES
1.Importantpointstoremember
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CONCEPTFORJEE||ChapterCIRCLES
3.SOMEPARTICULARCASES
2.FindtheEquation;radius;centerofthecircleanditsxinterceptandyintercept?
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CONCEPTFORJEE||ChapterCIRCLES
4.GENERALEQUATIONOFCIRCLE
1.Theorem:-Provethattheequationx2 + y2 + 2gx + 2fy + c = 0
alwaysrepresentacirclewhosecentreis( - g; - f)andradius√g2 + f2
- c
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CONCEPTFORJEE||ChapterCIRCLES
5.DIFFERENTFORMSOFCIRCLE
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81.Diameterformofthecircle
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CONCEPTFORJEE||ChapterCIRCLES
5.DIFFERENTFORMSOFCIRCLE
2.Parametricformofcircle
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CONCEPTFORJEE||ChapterCIRCLES
5.DIFFERENTFORMSOFCIRCLE
3.Equationofacirclepassingthrough3points
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CONCEPTFORJEE||ChapterCIRCLES
5.DIFFERENTFORMSOFCIRCLE
4.Equationofacirclewithequationoftangentandradius
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CONCEPTFORJEE||ChapterCIRCLES
6.EQUATIONOFCIRCLEWITHTYPICALCONDITIONS
1.Equationwhenthecircletouchesthexaxisat (α;
0)andcutsoffinterceptontheyaxisoflength2l
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CONCEPTFORJEE||ChapterCIRCLES
6.EQUATIONOFCIRCLEWITHTYPICALCONDITIONS
2.Equationwhenthecircletouchestheyaxisat(0;
β)andcutsoffinterceptonthexaxisoflength2k.
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CONCEPTFORJEE||ChapterCIRCLES
7.POSITIONOFPOINTSWITHRESPECTTOACIRCLE
1.WhatisthePositionofpointwrttocircle
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CONCEPTFORJEE||ChapterCIRCLES
7.POSITIONOFPOINTSWITHRESPECTTOACIRCLE
2.Maximumandminimumdistanceofpointfromthecircle.
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CONCEPTFORJEE||ChapterCIRCLES
8.DIFFERENTCASESFORINTERSECTIONOFALINEANDACIRCLE
1.CHORD:IntersectionPointofLineandCircleareRealandDistinct.
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CONCEPTFORJEE||ChapterCIRCLES
8.DIFFERENTCASESFORINTERSECTIONOFALINEANDACIRCLE
2.TANGENT:IntersectionpointoflineandCircleareCoincident.
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CONCEPTFORJEE||ChapterCIRCLES
8.DIFFERENTCASESFORINTERSECTIONOFALINEANDACIRCLE
3.LineandCirclehaveNoIntersectionPoint.
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CONCEPTFORJEE||ChapterCIRCLES
9.TANGENTTOACIRCLEATAGIVENPOINT
1.SegmentofSecants;Chords;Tangent
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CONCEPTFORJEE||ChapterCIRCLES
9.TANGENTTOACIRCLEATAGIVENPOINT
2.Differentformoftheequationoftangent:-PointForm
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CONCEPTFORJEE||ChapterCIRCLES
9.TANGENTTOACIRCLEATAGIVENPOINT
3.Differentformoftheequationoftangent:-SlopeForm
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CONCEPTFORJEE||ChapterCIRCLES
9.TANGENTTOACIRCLEATAGIVENPOINT
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22 4.TangentsfromaPointOutsidethecircle.
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CONCEPTFORJEE||ChapterCIRCLES
9.TANGENTTOACIRCLEATAGIVENPOINT
5.LengthoftangentfromaPointtoaCircle.
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CONCEPTFORJEE||ChapterCIRCLES
9.TANGENTTOACIRCLEATAGIVENPOINT
6.Conditionforwhichcirclecanbedrawninquadrilateral
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CONCEPTFORJEE||ChapterCIRCLES
9.TANGENTTOACIRCLEATAGIVENPOINT
7.Equationofpairoftangents
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CONCEPTFORJEE||ChapterCIRCLES
9.TANGENTTOACIRCLEATAGIVENPOINT
8.Locusofintersectionoftangentsifanglebetweentangentistheta
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CONCEPTFORJEE||ChapterCIRCLES
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2710.NORMALTOACIRCLEATAGIVENPOINT
1.EquationofnormalinPointform
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CONCEPTFORJEE||ChapterCIRCLES
11.CHORDOFCONTACT
1.Chordofcontactfromapoint
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CONCEPTFORJEE||ChapterCIRCLES
11.CHORDOFCONTACT
2.Equationofchordbisectedatgivenpoint
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CONCEPTFORJEE||ChapterCIRCLES
12.DIRECTORCIRCLEANDITSEQUATION
1.DirectorCircleandequation
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CONCEPTFORJEE||ChapterCIRCLES
13.DIFFERENTCASESOFTWOCIRCLES
1.CommonTangentsofTwoCircles-DirectandTransverseCommonTangent
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CONCEPTFORJEE||ChapterCIRCLES
13.DIFFERENTCASESOFTWOCIRCLES
2.No.ofDirectandTransverseCommonTangentsWhen C1C2 > r1 +
r2
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CONCEPTFORJEE||ChapterCIRCLES
13.DIFFERENTCASESOFTWOCIRCLES
3.No.ofDirectandTransverseCommonTangentsWhen C1C2 = r1 + r2
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CONCEPTFORJEE||ChapterCIRCLES
13.DIFFERENTCASESOFTWOCIRCLES
4.No.ofDirectandTransverseCommonTangentsWhen r1 - r2 < C1C2
< r1 + r2
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CONCEPTFORJEE||ChapterCIRCLES
13.DIFFERENTCASESOFTWOCIRCLES
5.No.ofDirectandTransverseCommonTangentsWhen C1C2 = r1 - r2
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CONCEPTFORJEE||ChapterCIRCLES
13.DIFFERENTCASESOFTWOCIRCLES
6.No.ofDirectandTransverseCommonTangentsWhen C1C2 < r1 -
r2
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CONCEPTFORJEE||ChapterCIRCLES
13.DIFFERENTCASESOFTWOCIRCLES
7.LengthofDirectandtransversecommontangent
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CONCEPTFORJEE||ChapterCIRCLES
13.DIFFERENTCASESOFTWOCIRCLES
8. Find all the common tangent to the circles x2 + y2 - 2x - 6y
+ 9 = 0 andx2 + y2 + 6x - 2y + 1 = 0. Find the length of the direct
common tangent and indirectcommontangent.
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CONCEPTFORJEE||ChapterCIRCLES
14.ANGLEOFINTERSECTIONOFTWOCIRCLES.
1.Angleofintersectionoftwocircleandorthogonalintersectionofcircles
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CONCEPTFORJEE||ChapterCIRCLES
15.ORTHOGONALINTERSECTIONOFCIRCLES
1.Ifnconsecutivecircletoucheachotherandhave2commontangentsthanrelationbetweenradiusofcircle.
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CONCEPTFORJEE||ChapterCIRCLES
16.PROPERTIESOFRADICALAXIS
1.(i)Theradicalaxisisperpendiculartothelinejoiningthecentresofthegivencircles.
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CONCEPTFORJEE||ChapterCIRCLES
16.PROPERTIESOFRADICALAXIS
2.(ii)Theradicalaxisbisectsthecommontangentsoftwocircles.
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CONCEPTFORJEE||ChapterCIRCLES
16.PROPERTIESOFRADICALAXIS
3.(iii)Iftwocirclescutathirdcircleorthogonally;thentheradicalaxisoftwocirclewillpassthroughthecenterofthethirdcircle.
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CONCEPTFORJEE||ChapterCIRCLES
16.PROPERTIESOFRADICALAXIS
4.(iv)Thepositionoftheradicalaxisofthetwocirclesgeometricallyisas:
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CONCEPTFORJEE||ChapterCIRCLES
17.RADICALCENTER
1.IntroductiontoRadicalCenter
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CONCEPTFORJEE||ChapterCIRCLES
18.COMMONCHORDOFTWOCIRCLES
1.Equationofcommonchordandlengthofcommonchord
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CONCEPTFORJEE||ChapterCIRCLES
19.FAMILYOFCIRCLES
1. Property 1: The equation of the family of circles passing
through the point ofintersectionoftwogivencircles.
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CONCEPTFORJEE||ChapterCIRCLES
19.FAMILYOFCIRCLES
2. Property 2: The equation of the family of circles passing
through the point ofintersectionoflineandcircle
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CONCEPTFORJEE||ChapterCIRCLES
19.FAMILYOFCIRCLES
3.Property3:Theequationofthefamilyofcirclestouchingthecirclesandlineattheirpointofcontactis
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CONCEPTFORJEE||ChapterCIRCLES
19.FAMILYOFCIRCLES
4.Property4:Theequationofthefamilyofcirclespassingthroughtwogivenpoints
P x1, y1 and Q x2, y2
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CONCEPTFORJEE||ChapterCIRCLES
19.FAMILYOFCIRCLES
6. Property 5:The equation of family of circlewhich touches y -
y1 = m x - x1 at
x1; y1 foranyfinitemis
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( ) ( )
( ) ( )( )
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CONCEPTFORJEE||ChapterCIRCLES
19.FAMILYOFCIRCLES
7.EquationofacirclecircumscribingatrianglewhosesidesareL1=0;L2=0andL3=0
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CONCEPTFORJEE||ChapterCIRCLES
20.RADICALAXIS
1.IntroductiontoRadicalAxis
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CONCEPTFORJEE||ChapterCIRCLES
21.PROPERTIESOFRADICALCENTER
1. The coordinates of the radical center can be found by solving
the equation`S_1=S_2=S_3
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CONCEPTFORJEE||ChapterCIRCLES
21.PROPERTIESOFRADICALCENTER
2. The radical center of the three circles described on the
sides of a triangle asdiametersistheorthocenterofatriangle.
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21.PROPERTIESOFRADICALCENTER
3.Theradicalcenterof threegivencircleswillbe thecenterofa
fourthcirclewhichcutsallthethreecirclesorthogonally.
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22.LIMITINGPOINT
1.Limitingpointsofthecoaxialsystem
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CONCEPTFORJEE||ChapterCIRCLES
22.LIMITINGPOINT
2.Systemofco-axialcircleswhosetwolimitingpointaregiven.
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CONCEPTFORJEE||ChapterCIRCLES
23.IMAGEOFTHECIRCLEBYTHELINEMIRROR
1.Introduction
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CONCEPTFORJEE||ChapterCIRCLES
24.POLEANDPOLAR
1.Definitionandmeaningofpoleandpolar
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24.POLEANDPOLAR
2.Propertiesandapplications
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25.Powerofapoint
1.PowerofaPointWithrespecttoCirclewhenpointisoutsideacircle
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CONCEPTFORJEE||ChapterCIRCLES
25.Powerofapoint
2.PowerofaPointWithrespecttoCirclewhenpointisinsideacircle
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26.INTERSECTIONWITHOTHERCONICS
1.INTERSECTIONOFCIRCLEWITHPARABOLA
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CONCEPTFORJEE||ChapterCIRCLES
26.INTERSECTIONWITHOTHERCONICS
2.INTERSECTIONOFCIRCLEWITHELLIPSE
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CONCEPTFORJEE||ChapterCIRCLES
26.INTERSECTIONWITHOTHERCONICS
3.INTERSECTIONOFCIRCLEWITHHYPERBOLA
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CONCEPTFORJEE||ChapterCIRCLES
26.INTERSECTIONWITHOTHERCONICS
4.INTERSECTIONOFCIRCLEWITHOTHERCURVES
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