Find the equation of the parabola with focus | vedclass

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Question

(A) The focus of the parabola is $(0, -3)$ and the directrix is $y = 3$.Since the focus lies on the $y$-axis and the directrix is a horizontal line,th

Vedclass · Accepted Answer

$x^2 = -12y$

Vedclass · Answer

(A) The focus of the parabola is $(0, -3)$ and the directrix is $y = 3$.Since the focus lies on the $y$-axis and the directrix is a horizontal line,the parabola is symmetric about the $y$-axis.The standard form of such a parabola is $x^2 = 4ay$.The focus is $(0, a)$ and the directrix is $y = -a$.Comparing $(0, -3)$ with $(0, a)$,we get $a = -3$.Substituting $a = -3$ into the equation $x^2 = 4ay$,we get $x^2 = 4(-3)y$,which simplifies to $x^2 = -12y$.

Find the equation of the parabola with focus $(0, -3)$ and directrix $y = 3$.

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