Respuesta :
Answer:
[tex]y^2 =4(-9)(x-5)=-36 (X-5)[/tex]
[tex]y^2 = -36x +180[/tex]
[tex]y^2 +36x -180=0[/tex]
Step-by-step explanation:
For this case we have the following info:
Vertex =(5,0) = (h,k) let be the coordinates
Focus=(-4,0)=(h+p ,k) let be the coordinates
On this case since the y coordinates is always 0 we know that the parabola is on the x axis and k=0. Since the coordinate for th focus is less than the coordinate for the vertex we know that the parabola open to the left of th x axis.
And the general equation for a parabola with opens on the x axis is given by this equation:
[tex](y-k)^2 =4p(x-h)[/tex]
Since k =0 then [tex]y^2 =4p(x-h)[/tex] the value for h is given by the vertex on this case h=5, and we have this:
[tex]y^2 =4p(x-5)[/tex]
We can use the point of the focus in order to find the value of p who represent the value in order to find the directirx line for the parabola. If we replace (-4,0) into the equation we got:
h+p = -4 , 5+p =-4 so then p -4-5 = -9, and makes sense since the parabola opens to the left.
So then our equation would be given by:
[tex]y^2 =4(-9)(x-5)=-36 (X-5)[/tex]
[tex]y^2 = -36x +180[/tex]
[tex]y^2 +36x -180=0[/tex]
