The vertex of a parabola is (2, 2) and the coordinats of its two extremities of latus rectum are `(-2,0)` and (6, 0). Then find the equation of the parabola.

Answer

`(x-2)^(2)=-8(y-2)`

Explanation

Focus is midpoint of the extremities of latus rectum.
Thus, focus is (2,0).
Distance between focus and vertex is a=2.
Also, axis of the parabola is x=2 and parabola is concave downward as focus lies below the vertex.
Therefore, using equation `(x-h)^(2)=-4a(y-k)`, required equation of parabola is
`(x-2)^(2)=-8(y-2)`