Question

Find the equation of the parabola with focus (0,2) and directrix y = -2

Answer 1

Basically you are given two points (0, 2) and (x, -2). You can insert them in to the formula:

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


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

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

And expands to:
\(x^2 + y^2 - 4y + 4 = y^2 + 4y + 4\)

From here, you can cancel terms and finish solving for y