eliminate the parameter t to obtain an x-y equation from the two parametric equations: x=4cost and y=2sint

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- May 25th 2009, 10:39 PMtomatoeseliminating the parameter to obtain an x-y equation
eliminate the parameter t to obtain an x-y equation from the two parametric equations: x=4cost and y=2sint

- May 26th 2009, 01:25 AMearboth
1. You are supposed to know that $\displaystyle \sin^2(t)+\cos^2(t)=1$

2. $\displaystyle

\begin{array}{l}x=4\cos(t)\\ y=2\sin(t)\end{array}~\implies~\begin{array}{l}\le ft(\dfrac x4\right)^2=\cos^2(t)\\ \left( \dfrac y2\right)^2=\sin^2(t)\end{array}$

3. Now add columnwise:

$\displaystyle \dfrac{x^2}{16}+\dfrac{y^2}{4} = 1$