SOLUTION: Find a polar equation of a hyperbola with its focus at the pole, an eccentricity of e ={{{5/2}}}, and directrix at {{{y=4}}}, thank you.

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Question 1081076: Find a polar equation of a hyperbola with its focus at the pole, an eccentricity of e =5%2F2, and directrix at y=4, thank you.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
e+=5%2F2, and directrix at y=4

The standard form for the polar conics is:
r+=+ep%2F%281+%2B+e%2Asin%28theta%29%29

r+=+%285%2F2%294+%2F+%281+%2B+%285%2F2%29sin%28theta%29%29

r+=+%285%2Fcross%282%29%29cross%284%292+%2F+%281+%2B+%285%2F2%29sin%28theta%29%29

r+=+%285%2A2%29+%2F+%281+%2B+%285%2F2%29sin%28theta%29%29

r+=+10+%2F+%281+%2B+%285%2F2%29sin%28theta%29%29
to make it clear what the parameters are,
or, if you dislike fractions,

r+=+10+%2F+%281%2F2%29%282+%2B+5sin%28theta%29%29

r+=+10%2A2%2F%282%2B5sin%28theta%29%29

r+=+20%2F%282%2B5sin%28theta%29%29