Question

Let P(a , b) be a point on the parabola y 2 = 8 x such that the tangent at P passes through the centre of the circle x 2 + y 2 - 10 x - 14 y + 65 = 0. Let A be the product of all possible values of a and B be the product of all possible values of b. Then the value of A + B is equal to

• A. 0
• B. 25
• C. 40
• D. 65

Answer 1

Answer: (D)

65

Answer 2

The correct answer is (D):
Centre of circle x 2 + y 2 – 10 x –14 y + 65 = 0 is at (5, 7).
Let the equation of tangent to y 2 = 8 x is
yt = x + 2 t 2
which passes through (5, 7)
7 t = 5 + 2 t 2
⇒ 2 t 2 – 7 t + 5 = 0
t = 1, $\frac{5}{2}$
A = 1×12×2×($\frac{5}{2}$)2
= 25
B = 2×2×1×2×2×$\frac{5}{2}$
= 40
A+B = 65