Find the equation of the parabola with vertex | vedclass

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Question

(A) The vertex of the parabola is at $(0, 0)$ and the focus is at $(0, 2)$.Since the focus lies on the $y$-axis,the axis of the parabola is the $y$-ax

Vedclass · Accepted Answer

$x^{2} = 8y$

Vedclass · Answer

(A) The vertex of the parabola is at $(0, 0)$ and the focus is at $(0, 2)$.Since the focus lies on the $y$-axis,the axis of the parabola is the $y$-axis.The standard form of the equation of such a parabola is $x^{2} = 4ay$.Here,the distance from the vertex to the focus is $a = 2$.Substituting $a = 2$ into the equation,we get $x^{2} = 4(2)y$,which simplifies to $x^{2} = 8y$.

Find the equation of the parabola with vertex at $(0, 0)$ and focus at $(0, 2)$.

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