How do you find the eccentricity, directrix, focus and classify the conic section r=14.424.8cosθ?

1 Answer
Sep 19, 2016

See below.

Explanation:

We have

r=abccosθ or

x2+y2=abcxx2+y2 or

x2+y2=ax2+y2bx2+y2cx or

1=abx2+y2cx or
bx2+y2cx=a or

x2+y2=(cx+a)2b2 or

(1c2b2)x2+y22acb2x=a2b2

so we have supposing b0

c=b parabola
c>b hyperbola
c<b ellipse
c=0 circle