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