Verified answer

x=rcosθ, and since secθ=1/cosθ and cscθ=1/sinθ, x=1/sinθ so sinθ=1/x

y=rsinθ=1//cosθ so cosθ=1/y. Use the identity sin^2(θ)+cos2(θ)=1 and you should

get the required equation which can be written x^2+y^2=x^2y^2, or y^2=x^2/(x^2-1).

You should try and sketch the graph. Note that since |sinθ| and |cosθ| are both <=1

|x| and |y| are >=1. so (0,0) does not lie on the graph.