What is the equation of parabola whose vertex is at (0, 0) and focus is at (0, -2) ?

y^{2} + 8 x = 0

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y^{2} - 8 x = 0

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x^{2} + 8 y = 0

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x^{2} - 8 y = 0

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Solution

The correct option is D $x^{2} + 8 y = 0$
It is a downward opening parabola with general equation $x^{2} = 4 p y$
Given : Focus $= (0, - 2)$
We know that, Focus $= (0, p)$
$\Rightarrow p = - 2$
So, equation of parabola becomes
$x^{2} = 4 (- 2) y$
$x^{2} = - 8 y$

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