Question

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

• A. $(2,4)$
• B. $(4,2)$
• C. $(2,-9)$
• D. $(4,-2)$

Answer 1

Answer: (A)

$(2,4)$

The coordinates of the parabola which is open rightward and then equation $y^2=4ax$ is $(a,0)$.The focal distance of this parabola is $2a$.

Given equation of the parabola is $y^2=8x.$

Comparing this with the general equation of the parabola $y^2=4ax$.

$4ax=8x$

$\Rightarrow a=2$

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

$\Rightarrow y^2=16$

$\therefore y=\pm 4$ and $x=2$

Hence the coordinates are $(2,4)$ and $(2,-4)$