Write the equation for a parabola with a focus at (1,-4)(1,−4) and a directrix at x=2x=2.

Answer 1

We know that the distance from the vertex to both the focus and the directrix is p, so the vertex is halfway between the focus and the directrix.

 

We have a rotated parabola because the directrix is vertical. The focus is inside the parabola and the directrix is outside, so our parabola opens to the left.

 

The vertex is (1.5,-4), and p = .5, so the equation is...

 

(y - (-4))² = -4(.5)(x - 1.5)

(y + 4)² = -2(x - 1.5)

 

I hope this helps! Let me know if you need more information.