SOLUTION: Determine the eccentricity, type of conic, and the directrix. {{{ r=7/(4-2cos(theta)) }}}

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Determine the eccentricity, type of conic, and the directrix. {{{ r=7/(4-2cos(theta)) }}}      Log On


   

Question 1175623: Determine the eccentricity, type of conic, and the directrix.
+r=7%2F%284-2cos%28theta%29%29+
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
r=7%2F%284-2cos%28theta%29%29

polar equation is r+=+ed%2F%281+-+e%2Acos%28theta%29%29

in our case r=7%2F%284%281-%281%2F2%29cos%28theta%29%29%29

from here eccentricity

e+=+1%2F2 => ellipse

ed+=+7%2F4+

%281%2F2%29d+=+7%2F4

d=%287%2F4%29%2F%281%2F2%29

d+=+7%2F2+

and equation of directrix x+=+-7%2F2