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!
$\displaystyle x = 2\cos^{2} r \quad \Rightarrow \quad \frac{x}{2} = \cos^{2} r$
$\displaystyle y = 3\sin^{2} r \quad \Rightarrow \quad \frac{y}{3} = \sin^{2} r$
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.