Hmmm. The standard form for the polar conics is
r = ep/(1 + e sinθ)
While your equation looks correct, I'd have written it as
r = (5/2) / (1 + (5/4) sinθ)
to make it clear what the parameters are. Or, if you dislike fractions,
r = 10/(4+5sinθ)
can you check my work?
Find a polar equation of a hyperbola with its focus at the pole, an eccentricity of e=5/4 and directrix at y=2.
answer: r=ek/1+esintheta
r=(5/4*2)/1+5/4sin theta
r=5/2(1+(5sintheta)/4)
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