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# Geometry problem

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What is the equation of a parabola with (−2, 4)  as its focus and y = 6 as its directrix?

Gwendolynkristine  Jun 5, 2017

#1
+89775
+1

Since the focus is below the directrix, this parabola turns downward

The  vertex  is given by   ( -2, [ 6 + 4] / 2)   =  ( -2, 5)

And p   =   (5 - 6)  = -1

So the equation becomes

4p( y - k) =  (x - h)^2   where  (h, k)  is the vertex  and p = -1

So we have

4(-1) (y - 5) = ( x  + 2) ^2

-4(y - 5)  =  ( x + 2) ^2

Here is the graph :  https://www.desmos.com/calculator/8iug8y6j5h

CPhill  Jun 5, 2017
#1
+89775
+1

Since the focus is below the directrix, this parabola turns downward

The  vertex  is given by   ( -2, [ 6 + 4] / 2)   =  ( -2, 5)

And p   =   (5 - 6)  = -1

So the equation becomes

4p( y - k) =  (x - h)^2   where  (h, k)  is the vertex  and p = -1

So we have

4(-1) (y - 5) = ( x  + 2) ^2

-4(y - 5)  =  ( x + 2) ^2

Here is the graph :  https://www.desmos.com/calculator/8iug8y6j5h

CPhill  Jun 5, 2017