The equation of the parabola with its vertex at the origin,... | MATH - PARABOLA | SolveeIt | Solveeit

Today, August 18

Question

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

$y ^ { 2 } = 12 x + 6$

B

$x ^ { 2 } = 12 y$

C

$x ^ { 2 } = - 12 y$

D

$y ^ { 2 } = - 12 x + 6$

Answer

$x ^ { 2 } = - 12 y$

Explanation

Solution

Since the axis of parabola is y-axis with its vertex at origin.

∴Equation of parabola $x ^ { 2 } = 4 a y$ . Since it passes through

(6, –3) ; ∴36= –12a ⇒ $a = - 3$

∴ Equation of parabola is $x ^ { 2 } = - 12 y$