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# Cartesian from parametric

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Find the Cartesian equation of the graph whose parametric equations are x=3cos(theta)-1 and y =4sin(theta)+1.

Guest Aug 14, 2017
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Find the Cartesian equation of the graph

whose parametric equations are

x=3cos(theta)-1 and

y =4sin(theta)+1.

$$\begin{array}{|rcll|} \hline & x &=& 3\cos(\theta)-1 \\ (1) & \frac{x+1}{3} &=& \cos(\theta) \\\\ & y &=& 4\sin(\theta)+1 \\ (2) & \frac{y-1}{4} &=& \sin(\theta) \\\\ \hline &&& \cos^2(\theta) + \sin^2(\theta) = 1 \\ & \left( \frac{x+1}{3} \right)^2 + \left( \frac{y-1}{4} \right)^2 &=& 1 \\\\ & \mathbf{ \frac{(x+1)^2}{3^2} + \frac{(y-1)^2}{4^2} } & \mathbf{=} & \mathbf{ 1 } & | \quad \text{ ellipse with center } (-1,1) \\ & && & | \quad \text{ and } a = 3 \text{ and } b=4 \\ \hline \end{array}$$

heureka  Aug 15, 2017