need help converting r= 2/1-cos ? to Cartesian equation

Question

need help converting r= 2/1-cos ? to Cartesian equation

Answer 1

In converting from polar to cartesian coordinates, the following equations are useful:

r = √(x² + y²)

x = r*cos(θ)

y = r*sin(θ)

 

We can multiply both sides of your equation by the denominator to yield

r[1 - cos(θ)] = 2.  Distributing, we have

r - r*cos(θ) = 2.  Convert from polar to cartesian by making appropriate substitutions:

√(x² + y²) - x = 2.  Add x to both sides:

√(x² + y²) = x + 2.  Square both sides:

x² + y² = x² + 4x + 4.  Subtract x² from both sides:

y² = 4x + 4.  Solve for x:

x = y²/4 - 1. 

 

This is a parabola whose line of symmetry is the x-axis.