Question

Find the standard form of the equation of the parabola with a focus at (0, -8) and a directrix at y = 8.

Answer 1

If you have two points, the focus \((x_1, y_1)\) and the directrix \((x_2, y_2)\), then you can insert both points in to the formula:

\((x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2\)

Answer 2

Here are the answer choices:
y =-1/32x^2

y^2 = -32x

y^2 = -8x

y =-/8x^2

Answer 3

So how I go about solving the problem now?

Answer 4

In this case, the focus is \((0,-8)\)
The directrix is \((0,8)\)

If you inserted the given points in to the equation, you'd have:

\((x - 0)^2 + (y - (-8))^2 = (x - x)^2 + (y - 8)^2\)

Answer 5

Then you'd simplify that to just

\(x^2 + (y + 8)^2 = (y - 8)^2\)

The next step is to expand the binomials and solve for y

Answer 6

Let me try that:3

Answer 7

Is the answer y =-1/32x^2

Answer 8

Show the work you did to arrive at that answer.