Question

How do you find the rectangular equation for `r=1/(4-costheta)`?

Answer 1

`x^2+y^2=((x+1)/4)^2` which is the equation of an ellipse.

Explanation:

`{(x=rcos theta),(y=rsin theta):}` so

`sqrt(x^2+y^2)=1/(4-x/sqrt(x^2+y^2))` or

`sqrt(x^2+y^2)=sqrt(x^2+y^2)/(4 sqrt(x^2+y^2)-x)` or

`4 sqrt(x^2+y^2)-x = 1` or

`sqrt(x^2+y^2) = (x+1)/4` Finally

`x^2+y^2=((x+1)/4)^2` which is the equation of an ellipse.