The equations to transform from Cartesian to polar :
x = r cos θ , y = r sin θ
Or
x² = r² cos² θ , y² = r² sin² θ
To represent the Cartesian equation x²−y²=1
substitute with the values of x² and y²
∴ r² cos² θ - r² sin² θ = 1
r² (cos² θ - sin² θ) = 1
but cos² θ - sin² θ = cos 2θ
∴ r² cos 2θ = 1
r² = 1/cos 2θ
∴ r² = sec 2θ ⇒⇒⇒⇒ The required equation
