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)

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