Question

The coordinates of a point on the parabola $y^2=8x$ whose focal distance is $4,$ is

• A. $(-2,-4),(2,-4)$
• B. $(2,4),(2,-4)$
• C. $(1,4),(2,-4)$
• D. $(2,-4),(-2,4)$

Answer 1

The correct option is B $(2,4),(2,-4)$

Given equation of parabola $y^2=8x$

General equation of parabola $y^2=4ax$

Comparing both the equation, we get

$4ax=8x$

$\Rightarrow a=2$

Let the required point be $(x_1,y_1)$.

Given that focal distance = 4

$\therefore x_1+a=4$

$\Rightarrow x_1=4-a=4-2=2$

$\therefore y^2=8\times 2=16$

$\Rightarrow y^2=\pm 4$

Hence the co-ordinates of the points are $(2,-4)$ and $(2,4)$.