# How do you convert r = 1/(1-cos(theta)) into cartesian form?

Aug 9, 2016

${y}^{2} = 2 x + 1$ representing the parabola with axis ax =-1/2 and focus at the origin.

#### Explanation:

The conversion formula is $\left(x , y\right) = \left(r \cos \theta , r \sin \theta\right)$.

The given equation is r = sqrt (x^2+y^2)=1/(1-x/sqrt(x^2+y^2)

Cross multiplying, rationalizing and simplifying,

${y}^{2} = 2 x + 1$

This is in the standard form of the equation of parabolas

${\left(y - \beta\right)}^{2} = 4 a \left(s - \alpha\right)$,

representing parabolas having vertex at (alpha, beta) parameter a

and focus at(alpha +a, beta)#.

Here, $a = \frac{1}{2} , \alpha = - \frac{1}{2} \mathmr{and} \beta = 0$...