JEE Main 2024 (Online) 4th April Morning ShiftQuestion 1
Let the length of the focal chord $PQ$ of the parabola $y^{2}=12x$ be $15$ units. If the distance of $PQ$ from the origin is $p$, then $10p^{2}$ is equal to $\_\_\_\_\_\_\_\_$ .
Parabola
Answer$72$
Solution
For $y^2=12x$ ($a=3$) a focal chord of slope $m$ has length $\frac{12(1+m^2)}{m^2}=15$, so $m^2=4$. The chord $2x-y-6=0$ is at distance $p=\frac6{\sqrt5}$ from $O$, so $10p^2=72$.