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Maths4Scotland HigherThe Circle The following questions are onNon-calculator questions will be indicatedClick to continueYou will need a pencil, paper, ruler and rubber.

Maths4Scotland HigherPreviousNextQuitQuitFind the equation of the circle with centre(3, 4) and passing through the origin. Find radius (distance formula):You know the centre:Write down equation:

Maths4Scotland HigherPreviousNextQuitQuitExplain why the equationdoes not represent a circle. Consider the 2 conditionsCalculate g and f:1. Coefficients of x2 and y2 must be the same.2. Radius must be > 0Deduction:Equation does not represent a circle

Maths4Scotland HigherPreviousNextQuitQuitCalculate mid-point for centre:Calculate radius CQ:Write down equation;Find the equation of the circle which has P(2, 1) and Q(4, 5)as the end points of a diameter. Make a sketch

Maths4Scotland HigherPreviousNextQuitQuitCalculate centre of circle:Calculate gradient of OP (radius to tangent)Gradient of tangent:Find the equation of the tangent at the point (3, 4) on the circle Equation of tangent:Make a sketch

Maths4Scotland HigherPreviousNextQuitQuitFind centre of circle:Calculate gradient of radius to tangentGradient of tangent:The point P(2, 3) lies on the circleFind the equation of the tangent at P.Equation of tangent:Make a sketch

Maths4Scotland HigherPreviousNextQuitQuitA is centre of small circleO, A and B are the centres of the three circles shown inthe diagram. The two outer circles are congruent, eachtouches the smallest circle. Circle centre A has equation The three centres lie on a parabola whose axis of symmetryis shown the by broken line through A. a) i) State coordinates of A and find length of line OA. ii) Hence find the equation of the circle with centre B. b) The equation of the parabola can be written in the form Find OA (Distance formula)Find radius of circle A from eqn.Use symmetry, find BFind radius of circle BFind p and q.Eqn. of BPoints O, A, B lie on parabola subst. A and B in turnSolve:

Maths4Scotland HigherPreviousNextQuitQuitFind centre of circle P:Gradient of radius of Q to tangent:Equation of tangent:Solve eqns. simultaneouslyFind radius of circle :P:Find distance between centresDeduction:= sum of radii, so circles touchGradient tangent at Q:Soln:

Maths4Scotland HigherPreviousNextQuitQuitFor what range of values of k does the equation represent a circle ? Determine g, f and c:State conditionPut in valuesSimplifyComplete the squareSo equation is a circle for all values of k.Need to see the positionof the parabolaMinimum value isThis is positive, so graph is:

Maths4Scotland HigherPreviousNextQuitQuitFor what range of values of c does the equation represent a circle ? Determine g, f and c:State conditionPut in valuesSimplifyRe-arrange:

Maths4Scotland HigherPreviousNextQuitQuitThe circle shown has equation Find the equation of the tangent at the point (6, 2). Calculate centre of circle:Calculate gradient of radius (to tangent)Gradient of tangent:Equation of tangent:

Maths4Scotland HigherPreviousNextQuitQuitFind centre and radius of Circle AFind centre and radius of Circle CFind distance AB (distance formula)Find diameter of circle BUse proportion to find BCentre of BEquation of B

Maths4Scotland HigherPreviousQuitQuitYou have completed all 11 questions in this presentationBack to start

Maths4Scotland HigherReturnTable of exact values

304560

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