derive the equation of the parabola with a focus at (4,-7) and a directrix of y= -15 put the equation in standard form

Answer 1

The basic equations are:

(x - h)² = 4p (y - k) and (y - k)² = 4p (x - h)

When I sketch the directrix and the focus, this shows that the parabola opens up. This means it would use this version of the equation.

(x - h)² = 4p (y - k)

The vertex is (h,k). The vertex would be half way between the focus and the directrix. This would be (4,-11) The p value is the distance between the vertex and the focus and the vertex and the directrix (It should be the same). In this case, 4. Plugging all this in.

(x - 4)² = 4(4) (y - (-11)) Simplify

(x - 4)² = 16 (y+11)