Write the equation for a parabola with a focus at (5,-5) and a directrix at y= -4

y = (-1/2)(x-5)^2 - 4.5

Step-by-step explanation:

The general formula for a vertical parabola is 4py=x^2.

Here the vertex is not at (0,0), but rather is at (5, -4.5) (halfway between the focus and the directrix).  The graph of the parabola opens down, because the directrix is higher up the y-axis than the focus.

Thus, this equation becomes 4p(x+4.5) = (x-5)^2.

Here p = half the distance between the focus and the directrix, or 0.5.  Because the graph opens downward, use p = -0.5.

Then we have 4(-0.5)(y+4.5) = (x-5)^2, or

                            -2   (y + 4.5) = (x-5)^2, or

                                    y + 4.5 = (-1/2)(x-5)^2, or

                                     y = (-1/2)(x-5)^2 - 4.5

answer: 20

step-by-step explanation: