Topical Revision Paper 10 Unit 10 Circles Students

Topical Revision Paper 10 Term 3 Unit 10: Points, Lines and Shapes Question 1: The equation of a circle C1 is 22 20 4 100 0x y x y     . Find (i) the radius and the coordinates of the centre of the circle, [2] (ii) the value(s) of k if the circle touches the line yk . [2] (iii) the equation of the another circle, C2 that has the same centre as C1, and passes through the point ( 11,2) . [2] Answer : (i) Centre : ( 10,2) and Radius = 2 units (ii) k = 0 or 4 (iii) Equation of circle C2 : 22( 10) ( 2) 1xy    [Standard Form] Or Equation of circle C2 : 22 20 4 103 0x y x y     [General Form] Question 2: The diagram shows two circles C1 and C2 centred at A and B respectively. C1 passes through O and P and touches C2 at R. Q is on C2 such that QB is parallel to the y-axis. The length of PQ is 12 units and PQ is a tangent to both circles. Given that the equation of C1 is 22 18 0x y y   , find (i) the centre and radius of C1 , [3]

(ii) the equation of C2 , [4] (iii) the equation of the perpendicular bisector of AB. [4] Answer: (i)  1The centre of : 0, 9C (ii)     22 2 2The equation of is 12 14 4C x y     [Standard Form] OR 22 2The equation of is x 24 28 384 0C y x y      [General Form] (iii) 12 259 5 10yx  Question 3: The equation of a circle, C, is given by 22 4 10 0x y x y m     where m is a constant. A line 24yx is a tangent to the circle. (i) Write down the coordinates of the centre, O, of the circle. [1] (ii) Find the radius of the circle and the value of m. [5] (iii) The circle, C, is reflected in the line 24yx . Find the equation of the reflected circle. [3] Answer: (i) (2,5) (ii) 24 Radius = 5 unitsm (ii) 22 22 ( 6) +( 3) = 10 or 16 6 + 53 = 0 xy x y x y     Question 4: (i) The equation of a circle is given by 22 10 2 1 0x y x y     . Find the centre and the radius of the circle. [2] (ii) The tangent to the circle at a point A is parallel to the straight line 20xy . Find the equation of the diameter of the circle through A. [2] (iii) The circle is then reflected about the y-axis. State the equation of the new circle formed. [1] Answer: (i) Centre is (5, -1) and the radius is 5 units (ii) 4yx  (iii) 2 2 2( 5) ( 1) 5xy    OR 22 10 2 1 0x y x y    