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 $k$ ?

Question

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 ?

Aicharya · Accepted Answer

Equation of chord with mid point ( h , &#160; k ) : k . y - 16 x + h 2 = k 2 - 16 h &#8658; 8 x - k y + k 2 - 8 h = 0 &#160; Comparing with 2 x + y - p = 0 , we get k = - 4 ; 2 h - p = 4 Only p = 2 , &#160; h = 3 , &#160; k = - 4 satisfies above relation.

If a chord, which is not a tangent, of the parabola y 2 = 16 x has the equation 2 x + y = p , and midpoint…

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