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Q.
Find the equation of the parabola with vertex at $(0,0)$ and focus at $(0,2)$.
Conic Sections
Solution:
Since the vertex is at $(0, 0)$ and the focus is at $(0, 2)$ which lies on $y$-axis, the $y$-axis is the axis of the parabola. Therefore, equation of the parabola is of the form $x^{2 }= 4ay$, thus, we have $x^{2} = 4(2)y$, i.e., $x^{2} = 8 y$.