Which of the following polar equations produces the same graph as the Cartesian equation x2 - y2 = 16?

Question

 Which of the following polar equations produces the same graph as the Cartesian equation x² - y² = 16?

A	r = 4
B	r2 cos θ = 16
C	r cos θ = 16
D	r2 cos 2θ = 16

Answer 1

x = rcosθ and y = rsinθ

So, x² - y² = 16 can be rewritten as r²cos²θ - r²sin²θ = 16

r² (cos²θ - sin²θ) = 16

r²cos(2θ) = 16