Question

For the given curve $y^2=8x$, which of the following statements are correct?

I. Length of the latus rectum $8$.
II. Focal distance to the point $(2,4)$ is $4$.
III. One of the points on the curve is $(2,-4).$

• A. Only I and III
• B. Only II and III
• C. Only I and II
• D. All the three

Answer 1

The correct option is D All the three

$y^2=8x$
$4a=8$
$a=2$
$f=(2,0)$
L.R $=4a=8$
Focal distance of $(2,4)$ $=\sqrt{(2-2{)}^2+(4-0{)}^2}=4$
$S=y^2-8x$
$S_{(2,-4)}=0$
$\Rightarrow (2,-4)$ lies on the curve.