Correct option (a) 2x –y+1 = 0
Explanation:
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).
3 - m + 2/m2 - 3m + 2 = 0
(m - 2)(m -1) = 0
m = 1, 2
y = x + 2 or y = 2x + 1