given-the-parametric-equations-x5costx5cost-and-y2sinty2sint-for-tt-in-the-inter

Question

Given the parametric equations $x=5\cos(t)$ and $y=2\sin(t)$ for $t$ $\in$ $[0,2\pi]$ , graph the corresponding plane curve. What is the rectangular equation of this curve?

Accepted Answer

$\frac{x^2}{25}+\frac{y^2}{4}=1$

Graph of a parametric equation showing another ellipse in blue on a grid.

Answer

$\frac{x^2}{25}+\frac{y^2}{4}=1$

Graph of a parametric equation showing a hyperbola in blue on a grid.

Answer

$\frac{x^2}{25}+\frac{y^2}{4}=1$

Graph of a parametric equation showing a different hyperbola in blue on a grid.

Answer

$\frac{x^2}{25}+\frac{y^2}{4}=1$

Graph of a parametric equation showing an ellipse in blue on a grid.

Given the parametric equations x=5cos(t)x=5\cos(t)x=5cos(t) and y=2sin(t)y=2\sin(t)y=2sin(t) for ttt ∈\in [0,2π][0,2\pi][0,2π], graph the corresponding plane curve. What is the rectangular equation of this curve?

Given the parametric equations $x=5\cos(t)$ and $y=2\sin(t)$ for $t$ $\in$ $[0,2\pi]$ , graph the corresponding plane curve. What is the rectangular equation of this curve?