Q. The equation of the parabola with its vertex at the origin, axis on the $y$-axis and passing through the point $(6, - 3)$ is
A) $y^{2} = 12x + 6$
B) $x^{2} = 12y$
C) $x^{2} = - 12y$
D) $y^{2} = - 12x + 6$
Explanation
(c)
Given that, the axis of parabola is $y$-axis and vertex is origin
$\therefore$ Equation of parabola is $x^{2} = 4ay$
Since, it passes through $(6,\ - 3)$
$\therefore{(6)}^{2} = 4a( - 3)$
$\Rightarrow 36 = - 12a \Rightarrow a = - 3$
$\therefore$ Equation of parabola is $x^{2} = - 12y$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.