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. $20$
• D. $22$

Answer 1

Answer: (A)

$25$

$y^2=4ax=16x\Rightarrow a=4$
$A(1,4)\Rightarrow \mathrm{2.4.}{t}_1=4\Rightarrow t_1=\frac{1}{2}$
$\therefore$ length of focal chord $=a{(t+\frac{1}{t})}^2$
$=4{(\frac{1}{2}+2)}^2=4\cdot \frac{25}{4}=25$.