Question

Find the polar equation of the conic with focus at the pole, having eccentricity 5 and
directrix y = -6.

Thank you so Much!
recall that r = ed/(1-e cosθ) has
eccentricity e and directrix x = d
so, r = 5*6/(1-5cosθ)
has directrix x = 6
But your directrix is that line rotated 3π/2, so
r = 30/(1-5cos(θ-3π/2)) = 30/(1+5sinθ)

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