How do I solve the following problem?

Question

Convert the polar equation to rectangular coordinates (Use variables x and y as needed)
$r = \frac{3}{1 - cos θ}$ $r = 3/(1-costheta)$

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Answer 1 · 2018-02-26T05:35:10

We have that

$r \cdot (1 - cos θ) = 3$ $r*(1-costheta)=3$

$r - r \cdot cos θ = 3$ $r-r*costheta=3$

Because $x = r \cdot cos θ$ $x=r*costheta$ and $x^{2} + y^{2} = r^{2}$ $x^2+y^2=r^2$

Hence

$r - x = 3$ $r-x=3$

$r = x + 3$ $r=x+3$

$r^{2} = {(x + 3)}^{2}$ $r^2=(x+3)^2$

$x^{2} + y^{2} = x^{2} + 6 x + 9$ $x^2+y^2=x^2+6x+9$

$y^{2} = 6 \cdot x + 9$ $y^2=6*x+9$