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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

Best Answer 

 #1
avatar+87301 
+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

 

 

cool cool cool

CPhill  Jun 5, 2017
 #1
avatar+87301 
+1
Best Answer

 

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

 

 

cool cool cool

CPhill  Jun 5, 2017

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