### Author Topic: Section 7.1 Q 11  (Read 1441 times)

#### Guanyao Liang

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##### Section 7.1 Q 11
« 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?

#### Monika Dydynski

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##### Re: Section 7.1 Q 11
« Reply #1 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.