Question

x^2−y^2=3

Write the answer in the form r^2=f(t) where t stands for θ. Find r^2

Answer 1

consider \(x=r\cos\theta,y=r\sin\theta\) we have $$x^2-y^2=3\\(r\cos\theta)^2-(r\sin\theta)^2=3\\r^2(\cos^2\theta-\sin^2\theta)=3\\r^2\cos(2\theta)=3\\r^2=3\sec(2\theta)$$

Answer 2

thank you so much your awesome!!!! I have some other calc questions if you can help?