what is the equation when the focus is (-5,0) and the vertex is (2,0)?

Question

focus (-5,0) 

vertex (2,0)

 

what is the equation?

Answer 1

The focus is to the left of the vertex and is always inside of the parabola, so the parabola opens to the left. There will be two y's for each x so the y's are squared.

 

The general form is 4p(x-h) = (y-k)^2 where p is the directed distance from the vertex to the focus.

 

4(-5-2)(x-2) = (y-0)^2

 

-28(x-2) = y^2

 

y^2 = -28x + 56

 

Play with the graph here:

http://ggbtu.be/m86044