Question

Consider the circle C: x² + y² -  6y + 4 = 0 and the parabola P: y² = x. Then

(A)  the number of common tangents to C and P is 3.

(B)  the number of common tangents to C and P is 2.

(C)  x - 2y + 1 = 0 is one of the common tangents.

(D)  x + 2y + 1 = 0 is also one of the common tangents.

Answer 1

Correct option  : (A), (C)

Explanation :

C: x² + (y - 3)² = 5. Let Q(t², t) be any point on the parabola y² = x so that the equation of the tangent at Q is x - 2ty + t² =  0 which touches the circle C. So

Hence, the number of common tangents is 3 and x - 2y + 1 = 0 is a common tangent when t = 1