Question

The coordinates of the point of contact of the tangent to the parabola y² = 16x, which is perpendicular to the line

2x – y + 5 = 0 are-

• A. (16, 16)
• B. (16, –16)
• C. (1, 4)
• D. (1, –4)

Answer 1

Answer: (B)

(16, –16)

Answer 2

y² = 16x ...(1)

4a = 16 ̃ a = 4

2x – y + 5 = 0 ...(2)

A line is perpendicular to the line (2)

is ̃ x + 2y + l = 0 ...(3)

̃ m = – $\frac{1}{2}$

Now, line (3) touches the parabola (1), so coordinate of the point of contact is

̃ P$\left( \frac{a}{m^{2}},\frac{2a}{m} \right)$ = (16, –16)