If the focus and vertex of a parabola are the points (0, 2) and (0, 4), respectively, then find the equation

Answer

`x^(2)+8y=32`

Explanation

Focus is (0,2) and vertex is (0,4).
so, axis of the parabola is y-axis.
Also, parabola is concave downward.
Distance between focus and directrix is a=2.
`:.` Latus rectum = 4a=8
So, using equation `(x-h)^(2)=4a(y-k)`, equation of parabola is `(x-0)^(2)=-8(y-4)`
`or" "x^(2)+8y=32`