Question:
If one end of a focal chord of the parabola, $y^{2}=16 x$ is at $(1,4)$, then the length of this focal chord is:
Correct Option: 1
Solution:
$\because y^{2}=16 x$
$\Rightarrow a=4$
One end of focal of the parabola is at $(1,4)$
$\because \mathrm{y}$ - coordinate of focal chord is $2 a t$
$\therefore 2 a t=4$
$\Rightarrow t=\frac{1}{2}$
Hence, the required length of focal chord
$=a\left(t+\frac{1}{t}\right)^{2}=4 \times\left(2+\frac{1}{2}\right)^{2}=25$