Question

Convert the equation to polar form. (use variables r and θ as needed.) x2 - y2 = 5

Answer 1

x²-y²=5
converting the above into polar form we shall have:
x=r cosθ; y=r sinθ
thus
x²-y²=5 will be written as:
(r cosθ)²-(r sinθ)²=5
r² cos²θ- r² sin²θ=5
factoring r² out we get:
r²(cos²θ- sin²θ)=5

using trigonometric identity:
cos²θ- sin²θ=cos(2θ)

thus the expression will be:

r²(cos (2θ))=5
r²=5/cos (2θ)
hence;
r=√[5/cos (2θ)]