Answer:
[tex]\left(\frac{x-2}{3} \right)^{2}+\left(\frac{y+1}{2} \right)^{2} = 1[/tex] (An ellipse)
Step-by-step explanation:
Let consider the following trigonometric identity:
[tex]\sin^{2}\theta + \cos^{2}\theta = 1[/tex]
Each trigonometric function is cleared respectively in given parametric equations:
[tex]\cos \theta = \frac{x-2}{3}[/tex] and [tex]\sin \theta = \frac{y + 1}{2}[/tex]
The equivalent expression in rectangular form is:
[tex]\left(\frac{x-2}{3} \right)^{2}+\left(\frac{y+1}{2} \right)^{2} = 1[/tex]
Which represents an ellipse.
