Question

Find the distance between the points $(-acos\varphi ,bsin\varphi )$ and $(asin\varphi ,-bcos\varphi )$.

Answer 1

As we know that

Distance between two points $(x_1,y_1),(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

So distance between the points $(-a\cos \varphi ,b\sin \varphi ),(a\sin \varphi ,-b\cos \varphi )$ is $\sqrt{(-a\cos \varphi -a\sin \varphi {)}^2+(b\sin \varphi +b\cos \varphi {)}^2}=\sqrt{a^2+b^2}(\sin \varphi +\cos \varphi )$