Question

One extremity of a focal chord of the parabola $y^2=16x$ is A(1,4). Then the length of the focal chord at A is

• A. 25/4
• B. 25/2
• C. 15/2
• D. 25

Answer 1

The correct option is D

25

$y^2=16xa=4A=(1,4)=(a{t}^2,2at)$
$4t^2=1\Rightarrow t=\frac{1}{2}$
$AB=a(t+\frac{1}{t}{)}^2=4(2+\frac{1}{2}{)}^2=4\times \frac{25}{4}=25$