Question

Can somebody please teach me how to to math derivatives? I have read the lesson F.L.V.S. gave me several times but I still do not understand.
1. Derive the equation of the parabola with a focus at (4, −7) and a directrix of y = −15. Put the equation in standard form.
2. Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1.
3. Derive the equation of the parabola with a focus at (−7, 5) and a directrix of y = −11.
4. Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −1/2
I don't just want answers, I want to learn.

Answer 1

parabolas have a geometric interpretation:

it is the set of all points that are equal distance from a focus and a perpendicular line from the directrix