Gregg O. answered • 09/21/15

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

r = √(x

^{2}+ y^{2})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:

√(x

^{2}+ y^{2}) - x = 2. Add x to both sides:√(x

^{2}+ y^{2}) = x + 2. Square both sides:x

^{2}+ y^{2}= x^{2}+ 4x + 4. Subtract x^{2}from both sides:y

^{2}= 4x + 4. Solve for x:x = y

^{2}/4 - 1.This is a parabola whose line of symmetry is the x-axis.