can you check my work?

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)

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