Question

The points on the parabola $y^2=12x$ whose focal distance is 4, are

• A. $(2\sqrt{3},),(2,\sqrt{3})$
• B. $(1,2\sqrt{3}),(1,-2\sqrt{3})$
• C. $(1,2)$
• D. $Noneofthese$

Answer 1

The correct option is B $(1,2\sqrt{3}),(1,-2\sqrt{3})$

Focal distance of any point (x,y) on the parabola $y^2=4ax$ is given by x+a.
$a=3\Rightarrow abscissa\left(orx\right)is4-3=1and{y}^2=12,y=\pm 2\sqrt{3}$.
Hence points are $(1,2\sqrt{3}),(1,-2\sqrt{3})$.