Question

Please help me work through this math problem, thank you!

Answer 1

we have

`\begin{gathered} x=4\cos t \\ (x)/(4)=\cos t \end{gathered}`
`\begin{gathered} y=5\sin t \\ (y)/(5)=\sin t \end{gathered}`

squared both sides each equation

`\begin{gathered} (x^2)/(4^2)=\cos ^2t \\ \\ (y^2)/(5^2)=\sin ^2t \end{gathered}`

Adds both equations

`(x^2)/(16)+(y^2)/(25)=\cos ^2t+\sin ^2t`

Remember that

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

so

`(x^2)/(16)+(y^2)/(25)=1`

This is the equation of a vertical ellipse

see the figure below

The equation of a vertical ellipse with center at origin is equal to

`(x^2)/(b^2)+(y^2)/(a^2)=1`

where

a=5

b=4

center (0,0)