Answer:
[tex]9x^2+4y^2=36[/tex]
Step-by-step explanation:
We are given that
[tex]x=2cos t[/tex]
[tex]y=3 sin t[/tex]
[tex]0\leq t\leq 2\pi[/tex]
[tex]cost=\frac{x}{2}[/tex]
[tex]sint=\frac{y}{3}[/tex]
[tex]sin^2 t+cos^2 t=(\frac{x}{2})^2+(\frac{y}{3})^2[/tex]
[tex]1=\frac{x^2}{4}+\frac{y^2}{9}[/tex]
By using the formula
[tex]sin^2\theta+cos^2\theta=1[/tex]
[tex]1=\frac{9x^2+4y^2}{36}[/tex]
[tex]9x^2+4y^2=36[/tex]
