Express the parametric equations in rectangular (i.e., x-y) form. Graph these equations and...

Question:

Express the parametric equations in rectangular (i.e., x-y) form. Graph these equations and indicate the direction of the curve,

{eq}x(\theta) = 2 + \sin \theta \\ y(\theta) = -1 + 4 \cos \theta {/eq}

Parametric Equation:

We will eliminate the parameter to get the equation in terms of x and y that is we will use the trigonometric results to solve the problem.

Answer and Explanation:

To express the equation in the rectangular form we will eliminate the parameter:

{eq}x=2+\sin\theta\\ y=-1+4\cos\theta {/eq}

Now let s eliminate theta by rearranging the equation:

{eq}x-2=\sin\theta\\ \frac{y+1}{4}=\cos\theta {/eq}

Adding and squaring the above two equations:

{eq}(x-2)^{2}+\frac{(y+1)^{2}}{16}=1 {/eq}


Learn more about this topic:

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Graphs of Parametric Equations

from Precalculus: High School

Chapter 24 / Lesson 5
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