Q24 / 54 · JEE Advanced 2017 (Paper 1) · Mathematics

If a chord, which is not a tangent, of the parabola $y^{2} = 16 x$ has the equation $2 x + y = p$ , and midpoint (h, k), then which of the following is (are) possible value(s) of $p, h$ and $k$ ?

Solution

Equation of chord with mid point $(h, k)$ :

$k . y - 16 (\frac{x + h}{2}) = k^{2} - 16 h$

$\Rightarrow 8 x - k y + k^{2} - 8 h = 0$

Comparing with $2 x + y - p = 0,$ we get

$k = - 4; 2 h - p = 4$

Only $p = 2, h = 3, k = - 4$ satisfies above relation.

Hence, the correct answer is option: 'D'.