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)
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