Obtain cartesian equation of the curve

x= 2cos^(2)r

y= 3sin^(2)r

0 less than/equal R less than/equal to 2 pi

I dont know what to do....! Help me please!

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- Apr 17th 2008, 12:57 PMMathNeedy18Parametric Representation of a curve
Obtain cartesian equation of the curve

x= 2cos^(2)r

y= 3sin^(2)r

0 less than/equal R less than/equal to 2 pi

I dont know what to do....! Help me please! - Apr 17th 2008, 03:00 PMo_O
$\displaystyle x = 2\cos^{2} r \quad \Rightarrow \quad \frac{x}{2} = \cos^{2} r$

$\displaystyle y = 3\sin^{2} r \quad \Rightarrow \quad \frac{y}{3} = \sin^{2} r$

Add the equations:

$\displaystyle \frac{x}{2} + \frac{y}{3} = \underbrace{\cos^{2} r + \sin^{2} r}_{1}$

etc.

Make sure you pay attention to the restriction of r and how it affects the domain and range of the cartesian curve.