Find the Cartesian equation of x= 2cosecθ y= 2cotθ

Question

I really don't know how to start with this one. Any help appreciated.

Answer 1

recall the identity csc ^2 - 1= cot^2

Thus, as x/2 = csc θ, and y = 2 cot θ, we have y = 2 sqrt(x^2/4 - 1)

Note that the range of x is (-∞,-1] U [1, ∞)

Also, we let y = ± 2 sqrt(x^2/4 - 1)