Question

The directrix of a parabola is y=−4 . The focus of the parabola is (−2,−2) .

What is the equation of the parabola?

y=1/4(x+2)^2−3

y=1/8(x−2)^2−3

y=−1/8(x+2)^2+3

y=−1/4(x−2)^2−3

Answer 1

I am guessing you are to find it from First Principles

let P(x,y) be any point on it
Then
√( (x+2)^2 + (y+2)^2 ) = √(0^2 + (y+4)^2 )
square both sides and expand
x^2 + 4x + 4 + y^2 + 4y + 4 = y^2 + 8y + 16
x^2 + 4x - 8 = 4y
4y = x^2 + 4x + 4 - 4 - 8 , I completed the square
4y = (x+2)^2 - 12
y = (1/4)(x+2)^2 - 3