Question

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.

Answer 1

Vertex: (-5, 2)
Standard form of a vertical parabola
(x - h)^2 = 4p (y-k)
(x - (5))^2 = 4p (y -2)
(x + 5)^2 = 4p (y-2)
p is the distance between the vertex and either the focus or the directrix:
p = 3

Final equation:
(x +5)^2 = 4*3 (y-2)
(x + 5)^2 = 12 (y-2)