cartesian to polar χ²-2y²=4, I can´t understand

Answer 1

x² - 2y² = 4

Let x = rcosθ and y = rsinθ

Then, r²cos²θ - 2r²sin²θ = 4

r²cos²θ - 2r²(1 - cos²θ) = 4

r²(3cos²θ - 2) = 4

r² = 4 / (3cos²θ - 2)