Complete the general form of the equation using rectangular coordinates

Question

Write the given equation using rectangular coordinates (X,Y)

r= (3)/(1-cos theta)

0=? 

Answer 1

Taking Arturo's start

cos θ = x/r

r = 3 / (1 - x/r)

r(1 - x/r) = 3

r - x = 3

r = x + 3

r² = x² + 6x + 9

x² + y² = x² + 6x + 9

y² = 6x + 9

y² - 9 = 6x

(1/6)y² - 3/2 = x

parabola opening to the right.

Answer 2

r = 3/(1 - cosθ)

 

r = √(x² + y²)

 

cosθ = x/r = x/√(x² + y²)

 

√(x² + y²) = 3 / [1 - x/√(x² + y²)]

 

Not sure if this is what you are looking for, but you can perform additional algebra to get it in another form. 

 

Not sure what you meant by "0=?".