Question

Can you check my answers?
find two sets of parametric equations for the given rectangular equation
x+y^2=4


x=-y^2+4

y=-t^2
x=-t^2+4

x=-t^3
y=-t^3+4


Find a polar equation of an ellipse with its focus at the pole an eccentricity of e=1/4 and directrix at y=4.

answer: √(x^2 + y^2) / (y - 4) = 1/4

4√(x^2 + y^2) = y - 4

4r = r sin θ - 4

(sin θ - 4) r = 4

r = 4/(sin θ - 4)

Answer 1

the ellipse looks good, but

y=-t^2
x=-t^2+4

becomes

x-y=4
not x-y^2 = 4

same for t^3