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^{2} = 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 $x^{2} = - 12 y$
Parabola with axis on the y-axis and vertex at the origin is of the form $x^{2} = 4 a y$
It passes through (6, -3)
$∴ 36 = - 12 a \Rightarrow a = - 3$
$∴$ Equation of parabola is $x^{2} = - 12 y$

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