Eliminate θ from following equalities.

Question

x^²+y^²=16cos^²(θ)=[(16x^²)sin^²(θ)]/y^²

which is same as saying x^2+y^2=16cos^2(θ),,,,,and x^2+y^2=[(16x^2)sin^2(θ)]/y^2

y≠0

Answer is in form f(x,y)=0. That is a curve in xy plane.

Answer 1

(x-2)²+y²-4=0

is universe of points (y≠0) satisifying equalities

Answer 2

Start with

cos² θ = x² / r²

sin² θ = y² / r²

x² + y² = r²