Q. One of the points on the parabola $y^{2} = 12x$ with focal distance 12, is
A) $(3,\ 6)$
B) $(9,\ 6\sqrt{3)}$
C) $(7,\ 2\sqrt{21)}$
D) $(8,\ 4\sqrt{6}$)
Explanation
(b)
Let the point is
$\left( 3t^{2},\ 6t \right)$
$\therefore$ Focal distance $= \ 3t^{2}\ + 3$
$\Rightarrow 3t^{2} + 3\ = 12\$
$\Rightarrow 3t^{2} = 9\$
$\Rightarrow t^{2} = 3\$
$\Rightarrow t\ = \sqrt{3}$
Hence , the required point is
$(9,\ 6\sqrt{3})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.