Question

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

• A. $(4,6)$ and $(4,-6)$
• B. $(3,6)$ and $(3,-6)$
• C. $(3,5)$ and $(3,-5)$
• D. None of these

Answer 1

The correct option is B $(3,6)$ and $(3,-6)$

As we know that coordinates of the focus of parabola with equation $y^2=4ax$ are $(a,0)$.

The focal distance of this parabola is $2a$.

Given equation of parabola-

$y^2=12x.....\left(1\right)$

Comparing the above equation with general equation of parabola, we get

$\Rightarrow a=3$

We can say the points lie on point of intersection of latus rectum and the parabola.

Therefore,

Substituting $x=3$, we get

$y=\pm 6$

Hence the points will be $(3,6)$ and $(3,-6)$.