Question

Find the lengths of the normals drawn from the point on the axis of the parabola $y^2=8x$ whose distance from the focus is 8.

• A. 10
• B. 9
• C. 8
• D. None of these

Answer 1

The correct option is C 8

We have,

$y^2=8x$

On comparing that,

$y^2=4ax$

$a=2$

Then,

We know that,

$xt+y=4at+2t^3$

Then focus is $(2,0)$ and the point on the axis is $(10,0)$.

Then,

$10=2t^2+4$

$t^2=3$

Normal is at the point $(6,4\sqrt{3})$

The, required length is

$=\sqrt{{(10-6)}^2+{(4\sqrt{3}-0)}^2}$

$=\sqrt{4^2+48}$

$=\sqrt{64}$

$=8$

Hence, this is the answer.