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

f (x) = - 1/12 (x - 5) 2 + 2

f (x) = 1/12 (x - 5) 2 + 2

f (x) = - 1/12 (x + 5) 2 + 2

f (x) = 1/12 (x + 5) 2 + 2

From the given information, the parabola is a regular parabola facing up with vertex at (-5, 2).

Required equation is (x + 5) ^2 = 4p (y - 2)

But 2 + p = 5 = > p = 5 - 2 = 3

Therefore, required equation is (x + 5) ^2 = 4 (3) (y - 2)

(x + 5) ^2 = 12 (y - 2)

y - 2 = 1/12 (x + 5) ^2

y = 1/12 (x + 5) ^2 + 2

f (x) = 1/12 (x + 5) ^2 + 2