How do you find the cartesian equation for #r = 3 / (1 + cosT)#?

1 Answer
May 14, 2016

#y^2+6x-9=0#, representing a parabola, with vertex at #(3/2, 0)# and axis along x-axis in the negative x-direction.

Explanation:

Reading T as the polar coordinate #theta, cos theta=x/r and r^2=x^2+y^2#.

Now, the polar equation becomes #3-x = r = sqrt(x^2+y^2)#.

Squaring and simplifying, #y^2+6x-9=0#. The alternative standard

form is #y^2=-6(x-3/2)#, from which the characteristics of this parabola as given in the answer. .