write an equation for the parabola whose focus is (0,2) and whose directrix is x=2

Vertex is the mid point between focus and directrix.

=> Vertex = ( 1, 2 ).

Because the focus is on the left of the vertex, the parabola opens on the left.

General equation is this case is :

( y - k ) ^2 = 4a ( x - h ).

Where (h ,k) is the vertex.

|a| is the distance between focus and vertex = 1

Because parabola faces left, a = -1.

=> Equation is :

( y - 2 )^2 = -4 ( x - 1 )

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