Question

If one end of a focal chord of the parabola, $y^2=16x$ is at $(1,4)$, then the length of this focal chord is:

• A. $25$
• B. $24$
• C. $22$
• D. $20$

Answer 1

The correct option is A $25$

$y^2=4ax\Rightarrow y^2=16xa=4$

Let $A$ and $B$ be the end points of focal chord,
$A=(1,4)2at=4\Rightarrow 2\times 4\times t=4\Rightarrow t=\frac{1}{2}$
Also, the length of focal chord
$=a{(t+\frac{1}{t})}^2=4{(\frac{1}{2}+2)}^2=4\times \frac{25}{4}=25$