Question

Which equation in rectangular form describes the parametric equations x=2-3 cos t and y=1+4 sin t?​

Answer 1

The parametric equations represents an ellipse by the rectangular equation
`((x-2)^(2))/(9) + ((y-1)^(2))/(16) = 1`.

Explanation:

We proceed to use the following trigonometric identity to derive an expression in rectangular form:

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

Where:

`\cos t = (2-x)/(3)` and
`\sin t = (y-1)/(4)`

Then, we expand the expression as follows:

`((x-2)^(2))/(9) + ((y-1)^(2))/(16) = 1` (2)

The parametric equations represents an ellipse by the rectangular equation
`((x-2)^(2))/(9) + ((y-1)^(2))/(16) = 1`.