Toronto Math Forum
MAT2442018F => MAT244Lectures & Home Assignments => Topic started by: Guanyao Liang on November 02, 2018, 04:04:37 PM

Part c, how to know the graph of the solution in the (x1,x2) plane is a circle or an ellipse?

In this problem, $x_1=3\cos{2t}+4\sin{2t}$ and $x_2=\sin{2t}+4\cos{2t}$.
$${x_1}^2+{x_2}^2=(3\cos{2t}+4\sin{2t})^2+(\sin{2t}+4\cos{2t})^2=9(\cos^2{2t}+\sin^2{2t})+16(\cos^2{2t}+\sin^2{2t})=25$$
By definition, this is the equation of a circle centered at the origin with radius 5.