Question

A tangent to the parabola y² = 4ax makes an angle 45⁰ with the x-axis. Then its point of contact is

• A. (a, 2a)
• B. (-a, -2a)
• C. (a, -2a)
• D. (-a, 2a)

Answer 1

Answer: (A)

(a, 2a)

Answer 2

We know that the slope of the tangent at ‘t’ to the parabola y² = 4ax is 1/t.

∴ $\frac{1}{t}$ = tan45⁰ = 1 ⇒ t = 1

∴ The required point is (at², 2at) = (a, 2a)