What is the distance between the focus and th | vedclass

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(C) The given equation of the parabola is $x^2 = -8y$.Comparing this with the standard form $x^2 = -4ay$,we get $-4a = -8$,which implies $a = 2$.The f

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$4$

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(C) The given equation of the parabola is $x^2 = -8y$.Comparing this with the standard form $x^2 = -4ay$,we get $-4a = -8$,which implies $a = 2$.The focus of the parabola $x^2 = -4ay$ is $(0, -a)$ and the equation of the directrix is $y = a$.Here,the focus is $(0, -2)$ and the directrix is $y = 2$.The distance between the focus $(0, -2)$ and the directrix $y = 2$ is given by $|2 - (-2)| = |4| = 4$.Alternatively,the distance between the focus and the directrix of a parabola $x^2 = 4ay$ (or $x^2 = -4ay$) is $2a$.Substituting $a = 2$,the distance is $2 	imes 2 = 4$.

What is the distance between the focus and the directrix of the parabola $x^2 = -8y$?

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