Question

Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7

Answer 1

Answer: -1/24(x+5)^2+1

Answer 2

the main equation is y=a(x-h)²+k
the focus is (h, k+p), where p=1/4a
y=k-p
(h, k+p)=(−5, −5) ,
the derivative
y'=2a(x-h)
y'=-2/20(x+5)=(-1/10)(x+5)