Question

Tangent to the curve y=x^2 +6 at a point p(1,7) touches the circle x^2+y^2 +16x+12y+c=0 at a point q find the co ordinate of point q

Answer 1

Answer:

Equation of tangent to the parabola at (1, 7) is

x−(y+7)2+ 6 = ⇒ 2x – y + 5 = 0.

⇒ Centre ≡ (- 8, - 6)

Equation of CQ = x + 2y + k = 0

– 8 – 12 + k = 0 ⇒ k = 20

PQ ≡ 4x – 2y + 10 = 0

CQ ≡ x + 2y + 20 = 0

= 5x + 30 = 0 ⇒ x = - 6

⇒ – 6 + 2y + 20 = 0 ⇒ y = – 7

Hence the point of contact is (–6, –7).