The equation of the parabola with its vertex at the origin, axis on the y-axis

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

Options:

A .

y^{3} = 12 x + 6

B .

x^{2} = 12 y

C .

x^{2} = - 12 y

D .

y^{2} = - 12 x + 6

Answer: Option C
:
C

Since the axis of parabola is y-axis

$∴$ Equation of parabola $x^{2} = 4 a y$

Since it passes through (6 , -3)

$∴$ 36 = -12 a $\Rightarrow a = - 3$

∴

Equation of parabola is

x^{2} = - 12 y

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