Question

Let x² + y² + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x² at (2, 4). Then A + C is equal to______ . 

(A) 16 

(B) 88/5

(C) 72 

(D) –8

Answer 1

Correct option is (A) 16

x² + y² + Ax + By + C = 0 is passing through (0, 6) 

⇒ 6B + C = -36

The tangent of the parabola y = x² at (2, 4) is

4x - y - 4 = 0---(1)

The tangent of circle x² + y² + Ax + By + C = 0 at (2, 4) is

(4 + A) x + ( 8 + B)y + 2A + 4B + 2C = 0----(2)

From Equation (1) and (2)

\(\frac{4+A}4=\frac{8+B}{-1}=\frac{2A+4B+2C}{-4}\) 

A + 4B = -36---(3)

3A + 4B + 2C = -4----(4)

From equation (3) and (4)

A + C = 16