Question

The point of the contact of the tangent to the parabola y² = 4ax which makes an angle of 30° with X-axis, is

(a) (3a,2√3a) 

(b) (2√3a, 3a)

(c) (√3a, 6a) 

(d) None of these

Answer 1

 Correct option: (a) (3a,2√3a) 

Explanation:

Since tangent makes an angle of 30° with X-axis, so

Slope of tangent = tan 30° = 1/√3

Slope of tangent to the parabola at any point is given as:

dy/dx = 2a/y

Let (h, k) be any point on the parabola y² = 4ax which is point of contact of the tangent.

Slope of tangent to the parabola at point (h, k) is: