User:Egm6341.s10.team4.anandankala/HW7-9

=Parameterization of ellipse=

Given
$$\displaystyle x=a cost; y=b sint.$$

Prove That
$$\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2}=1$$

Solution
We have $$\displaystyle x=acost; y=bsint.$$

$$\displaystyle x=a cost \Rightarrow x^2=a^2(cost)^2$$

$$\displaystyle y=b sint \Rightarrow y^2=b^2(sint)^2$$

$$\displaystyle \Rightarrow \frac{x^2}{a^2}=(cost)^2 and \frac{y^2}{b^2}=(sint)^2 $$

$$\displaystyle \Rightarrow \frac{x^2}{a^2}+ \frac{y^2}{b^2}=(cost)^2+(sint)^2 $$

$$\displaystyle \Rightarrow \frac{x^2}{a^2}+ \frac{y^2}{b^2}= 1 $$