Answer:
[tex]r^2=4\sec 2\theta}[/tex]
Step-by-step explanation:
The given equation is:
[tex]x^2-y^2=4[/tex]
We substitute [tex]x=r\cos (\theta)[/tex] and [tex]y=r\sin (\theta)[/tex] to obtain:
[tex]r^2\cos^2\theta-r^2\sin^2\theta=4[/tex]
This implies that:
[tex]r^2(\cos^2\theta-\sin^2\theta)=4[/tex]
Apply double angle identity to obtain:
[tex]r^2\cos 2\theta=4[/tex]
This implies that:
[tex]r^2=\frac{4}{\cos 2\theta}[/tex]
This simplifies to:
[tex]r^2=4\sec 2\theta}[/tex]
