Question

Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1.

Answer 1

helpp please

Answer 2

This is deriving a quadratic equation from a parabola using distances right?
So use the combined distance formula. You need to use the combined distance formula because the points are in equal distance with the directrix.

\[\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(y_2-y_1)^2}\]

Simply plug in the coordinates of the focus on the left side of the equation. Plug in the directrix on the right side of the equation.

To solve this, you need to remove the radicals of the equations. Then, distribute y term binomials. After that, simplify and isolate x terms. Lastly, isolate the y term to receive the equation.