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

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the polar equation of the conic with focus at the pole, having eccentricity 5 and directrix y = -6.      Log On


   

Question 1136327: Find the polar equation of the conic with focus at the pole, having eccentricity 5 and
directrix y = -6.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
e=5=>e%3E0-> hyperbola
and directrix y+=+-6 =>horizontal main axis
d+ = distance between focus(pole) and directrix => distance from (0,0) to (0,-6) is 6
or, directrix y+=+-6=>y=+-d=>d=6
The sine function appears in the denominator, so the hyperbola is horizontal.
so, you will use formula +r+=++ed%2F%281-+e%2Asin%28theta%29%29
r+=++%286%2A5%29%2F%281-+5%2Asin%28theta%29%29
r+=++30%2F%281-5sin%28theta%29%29