How do you convert #r=100/(3-2costheta)# into cartesian form?

Question

1601 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-17T15:13:40

#2491x^2-9y^2-10000x+10000=0#

The given polar equation is in the form

#(a(1-e^2))/r=1-scos theta# that represents an ellipse with

eccentricity #e=2/3# ans semi major axis a = 60..

Use the conversion formula

#r(cos theta, sin theta)=(x, y)# that gives

#r =sqrt(x^2+y^2) and cos theta = x/r#.

Substituting and rearranging,

#3(sqrt(x^2+y^2))=50(2-x)#. Squaring and rearranging,

,#2491x^2-9y^2-10000x+10000=0#