The equation of the parabola with its vertex at the origin, axis on the y-axis and passing through the point (6, -3) is

$y^{3} = 12 x + 6$

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$x^{2} = 12 y$

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$x^{2} = - 12 y$

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

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Solution

The correct option is C
$x^{2} = - 12 y$

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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