Toronto Math Forum

MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: Guanyao Liang on November 02, 2018, 04:04:37 PM

Title: Section 7.1 Q 11
Post 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?

Title: Re: Section 7.1 Q 11
Post by: Monika Dydynski on November 02, 2018, 04:18:05 PM

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.