Which conic section has the polar equation $r=2/(3-cosq)$ ?

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Answer 1 · 2016-08-18T11:17:37

$8 x^2 + 9y^2-4 x-4=0$

From $r=2/(3-cosq)->3r-r cos q= 2$

but $r cos q = x$ and $r^2 = x^2+y^2$

so

$3 r - x = 2->r = (x+2)/3$ and also

$r^2 = x^2+y^2=(x+2)^2/9$

After some simplifications

$8 x^2 + 9y^2-4 x-4=0$

which is the equation of an ellipse

Which conic section has the polar equation r=2/(3-cosq)r=2/(3-cosq)?