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. $(1,2)$, $(2,1)$
• D. $(2,2\sqrt{3})$, $(2,-2\sqrt{3})$

Answer 1

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

Given equation of parabola is $y^2=12x.$

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

Then,

$4a=12$

$a=3$

$x+a=4$ focal distance is 4

$x+3=4$

$x=1$

put $x=1$ in given parabola equation

$\therefore y^2=12x$

$y^2=12\times 1$

$y^2=12$

$y=\pm 2\sqrt{3}$

And $x=1$

Hence, the coordinate are $(1,2\sqrt{3})$ and $(1,-2\sqrt{3})$.