Question

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

Answer 1

`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. .