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Find the equation of the parabola with v...

Find the equation of the parabola with vertex at (0,0) and focus at (0,2) Also, find the equation of its directrix.

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Let O(0,0) be the vertex and F(0,2) be the focus of the given parabola. Since focus lies on the y-axis, so y-axis is the axis of the parabola. Also, the focus lies above tha x-axis. So, it is a case of upward parabola. Let the equation of the parabola be `x^(2)=4ay`. Then, its focus is F(0,a) and so a=2. Hence the required equation is `x^(2)=8y`. Also, the equation of the directrix is y=-2
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