Question

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

Answer 1

Answer:

The parametric equations represents an ellipse by the rectangular equation $\frac{(x-2)^{2}}{9} + \frac{(y-1)^{2}}{16} = 1$.

Step-by-step 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:

$\cos t = \frac{2-x}{3}$ and $\sin t = \frac{y-1}{4}$

Then, we expand the expression as follows:

$\frac{(x-2)^{2}}{9} + \frac{(y-1)^{2}}{16} = 1$ (2)

The parametric equations represents an ellipse by the rectangular equation $\frac{(x-2)^{2}}{9} + \frac{(y-1)^{2}}{16} = 1$.