JEE Advanced 2017 Paper 1Question 1
If a chord, which is not a tangent, of the parabola $y^2=16x$ has the equation $2x+y=p$, and midpoint $(h,k)$, then which of the following is(are) possible value(s) of $p$, $h$ and $k$?
Parabola
Solution
Substituting $y=p-2x$: $4x^2-(4p+16)x+p^2=0$, so $h=\frac{p+4}2$, $k=p-2h=-4$. Non-tangent needs discriminant $>0$: $p>-2$. Only $p=2,h=3,k=-4$ fits.