Question

Write and equation of the parabola Focus:(0,-4) Directrix:y=4

Answer 1

y=-x²/16

Explanation:

Let's assume P(x,y) a point of the parabola,

H is the projection of P on x axis

F (0,-4) is the focus

PH²=PF²

`PH^2=(y-4)^2=y^2-8y+16\\PF^2=x^2+(y-(-4))^2=x^2+y^2+8y+16\\\\y^2-8y+16=x^2+y^2+8y+16\\\\-x^2=8y+8y\\\\\boxed{y=-(x^2)/(16)}`