Question

A circle of equation x² + y²+ Ax + By + C = 0 passes through (0.6) and touches the parabola y = x² at (2,4) then A + C is

(1) 16
(2) 25
(3) 32
(4) 4

Answer 1

Correct option is (1) 16

Equation of tangent to parabola at (2, 4) y - 4 = m(x - 2)

\(\frac{dy}{dx} = 2x\)

⇒ \(m = \left.\frac{dy}{dx}\right|_{(2,4)}=4\)

\(y -4 = 4 (x - 2)\)

⇒ \(4x - y - 4 =0\)

Let equation of circle \(S + \lambda L = 0\)

\((x - 2)^2 + (y - 4)^2 + \lambda(4x - y - 4) = 0\)

It passes through (0, 6)

⇒ \(4 + 4 + \lambda (0 - 6 - 4) = 0\)