Question

The point of contact of the tangent $x + 2y + 2 = 0$ with the parabola $x^2 = 16y$ is

• A. (2, - 2)
• B. (4, 1)
• C. (-4, 1)
• D. (8, 4)

Answer 1

Answer: (C)

(-4, 1)

Answer 2

The parabola is $x^2 = 16y$ ... (i)
and tangent with it is $x + 2y + 2 = 0$ ... (ii)
tangent at any point $(x_1, y_1)$ to (i) is given by,
$x x_1 = 8(y + y_1)$
$x x_1 - 8y - 8y_1 = 0$ ... (iii)
(ii) and (iii) represents same line, therefore they are identical.
$\frac{x_{1}}{1} = \frac{-8}{2} = \frac{-8y_{1}}{2} \Rightarrow x_{1} = -4, y_{1} = 1$
$\therefore$ Point of contact is (-4, 1)