Question

Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9

Answer 1

Insert points focus (0,-9) and directrix (x,9) in to the following formula:

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

Upon doing so you get:
\((x - 0)^2 + (y - (-9))^2 = (x - x)^2 + (y - 9)^2\)

Which simplifies to:
\(x^2 + (y + 9)^2 = (y - 9)^2\)

And expands to:
\(x^2 + y^2 + 18y + 81 = y^2 - 18y + 81\)

\(y^2\) and \(81\) cancels on both sides leaving just:

\(x^2 + 18y = -18y\)

\(x^2 = -36y\)

From here, you can isolate y to find the standard form of the equation of the parabola.

Answer 2

Oh so y=-1/36x^2

Answer 3

Thanks man I understand now