Question

derive the equation of a parabola with a focus at (-5, 5) and a directrix of y = -1

Answer 1

well it's always handy to graph the information



find the distance between the focus and directrix... this is 2a

where a is the focal length.

then find half the value, this will be a, the focal distance

the vertex will be a units below the focus.

the standard vertex form I use is

\[(x - h)^2 = 4a(y - k)\]

(h, k) is the vertex and a is the focal length.

you can then make y the subject.

hope it helps