# Thread: How do you find parametric equations for an ellipse?

1. ## How do you find parametric equations for an ellipse?

For example, how would I find the parametric equations for (x^2)/(25) + (y^2)/(81) = 1

2. Originally Posted by jamessmith
For example, how would I find the parametric equations for (x^2)/(25) + (y^2)/(81) = 1

An ellipse is really just a stretched circle right?

Well the most common parameterization for a circle is

$\displaystyle x=a\cos(t)$
$\displaystyle y=a\sin(t)$

where "a" is the radius of the circle

So if we wanna stretch it, we look at your equation. The biggest value that x takes on is 5 and the biggest value of y is 9

So the radii are $\displaystyle \sqrt{5}$ and 3

So this time we just make the parameterization

$\displaystyle x=a\cos(t)$
$\displaystyle y=b\sin(t)$

with $\displaystyle a=5$ and $\displaystyle b=9$

3. Originally Posted by jamessmith
For example, how would I find the parametric equations for (x^2)/(25) + (y^2)/(81) = 1

$\displaystyle x=5\cos t\,,\,\,y=9\sin t\,,\,\,0\leq t \leq 2\pi$

Tonio