Parabolas

[Hooty143]

Hello,
I am having a problem writing an equation in standard form.
The problem asks to find the equation in standard form of the parabola with focus (-2, 4) and directrix x=4.
I have tried it a few different ways to find the vertex (h, K) and come up with different numbers each time therefor making p hard to find. If any one could help that would be great!! Thank you!

 

[galactus]

The vertex of the parabola lies between the directrix and the focus.

Since the directrix is at x=4 and the focus at (-2,4), then the vertex is at (1,4).

The distance between the vertex and the focus is the same as between the vertex and the directrix.

This distance is 'p'. p is not hard to find. It is just half the distance between the x coordinates given for the focus and directrix.

(h,k) is the coordinates of the vertex in the standard form.

Standard form for this type of parabola is \(\displaystyle x=\frac{-1}{4p}(y-k)^{2}+h\).