Question

Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values or t.

x=2cost,y=3sin t,0≤t<2π

Answer 1

`9x^2+4y^2=36`

Explanation:

We are given that

`x=2cos t`

`y=3 sin t`

`0\leq t\leq 2\pi`

`cost=(x)/(2)`

`sint=(y)/(3)`

`sin^2 t+cos^2 t=((x)/(2))^2+((y)/(3))^2`

`1=(x^2)/(4)+(y^2)/(9)`

By using the formula

`sin^2\theta+cos^2\theta=1`

`1=(9x^2+4y^2)/(36)`

`9x^2+4y^2=36`