Question

For the parabola $y^2=8x$, the point $P$ whose focal distance is $8$, is

• A. $(2,4)$ or $(2,-4)$
• B. $(1,4)$ or $(1,-4)$
• C. $(2,8)$ or $(2,-8)$
• D. None of these

Answer 1

Answer: (A)

$(2,4)$ or $(2,-4)$

Consider the diagram shown below.

Let $S$ be the focus and $P$ and $Q$ be the points on parabola.

Given,

Focal length, $PQ=8$

We know that the standard equation of a parabola is,

$y^2=4ax$

Compare this with the given parabola.

$a=2$

Thus,

$S=(2,0)$

Therefore,

$P=(2,y_1)$

$Q=(2,y_2)$

Again,

$y^2=8x$

$y^2=8\times 2$

$y^2=16$

$y=-4,+4$

Therefore,

Coordinates of the points are $(2,4)$ and $(2,-4)$.