Question

What is the rectangular equivalence to the parametric equations?

Answer 1

Answer:

$\left(\frac{x-2}{3} \right)^{2}+\left(\frac{y+1}{2} \right)^{2} = 1$ (An ellipse)

Step-by-step explanation:

Let consider the following trigonometric identity:

$\sin^{2}\theta + \cos^{2}\theta = 1$

Each trigonometric function is cleared respectively in given parametric equations:

$\cos \theta = \frac{x-2}{3}$ and $\sin \theta = \frac{y + 1}{2}$

The equivalent expression in rectangular form is:

$\left(\frac{x-2}{3} \right)^{2}+\left(\frac{y+1}{2} \right)^{2} = 1$

Which represents an ellipse.