Question

The circle x² + y² – 2x – 6y + 2 = 0 intersects the parabola y² = 8x orthogonally at the point P. The equation of the tangent to the parabola at P can be

a. 2x – y + 1 = 0

b. 2x + y – 2 = 0

c. x + y – 4 = 0

d. x  – y – 4 = 0

Answer 1

Correct option is a. 2x – y + 1 = 0

Let y = mx + 2/m be tangent to y² = 8x. Since circle intersects the parabola orthogonally. So this tangent is the normal for the circle. Every normal of the circle passes through its centre. So centre (1, 3).