(a) 17. Finds circle equation (x 2)2 + (y 6)2 = (10 (–2))2 + (11 6)2 M1 Checks whether (10, 1) satisfies their circle equation M1 Obtains (x + 2)2 + (y 6)2 = 132 and checks that (10 + 2)2 + (1 6)2 = – – A1 (3) 132 and so states that (10, 1) lies on (*) C (b) radius gradient or (m) M1 Finds gradient perpendicular to their radius using M1 Finds (equation and) of tangent (see note below) M1 y-intercept Obtains a correct value for of their tangent, i.e. 35 or A1 y-intercept –23 Deduces gradient of second tangent M1 Finds (equation and) of second tangent M1 y-intercept So obtains distance 35 + 23 = 58 (*) A1 (7) PQ = (10 marks)
17. (a) Finds circle equation (x 2)2 + (y 6)2 = (10 (–2))2 + (11 6)2 M1 Checks whether (10, 1) satisfies their circle equation M1 Obtains (x + 2)2 + (y – 6)2 = 132 and checks that (10 + 2)2 + (1 – 6)2 = 132 and so states that (10, 1) lies on C (*) A1 (3) (b) radius gradient or (m) M1 Finds gradient perpendicular to their radius using M1 Finds (equation and) y-intercept of tangent (see note below) M1 Obtains a correct value for y-intercept of their tangent, i.e. 35 or –23 A1 Deduces gradient of second tangent M1 Finds (equation and) y-intercept of second tangent M1 So obtains distance PQ = 35 + 23 = 58 (*) A1 (7) (10 marks)