120937
Find the equation of the parabola with vertex at \((0,0)\) and focus at \((0,2)\).
1 \(x^2=8 y\)
2 \(x^2=2 y\)
3 \(y^2=4 x\)
4 \(y^2=8 x\)
Explanation:
A Since the vertex is at \((0,0)\) and the focus is at \((0,2)\) which lies on \(y\)-axis, therefore, equation of the parabola is of the form \(x^2=4 a y\).
Thus, we have \(x^2=4(2) y\), i.e., \(x^2=8 y\).