TITLE: How to parameterize an ellipse?
QUESTION [5 upvotes]: I need to parameterize the ellipse $\frac{x^2}{2}+y^2=2$, so this is how I proceed:
I know that $a=2$ and $b=1$ (where $a$ and $b$ are the axis of the ellipse), so I parameterize as:
\begin{cases}
x=a\cos(t)\\
y=b\sin(t)
\end{cases}
and I get
\begin{cases}
x=2\cos(t)\\
y=\sin(t)
\end{cases}
but if I plot the parameterized curve and the equation those are not the same, I think that the cause it's the $=2$ in the equation but I don't know how to put it into the parameterized ellipse, can someone help me?

REPLY [4 votes]: Divide by 2 and write the denominator of the $y$ term as $(\sqrt2)^2$:
$$\frac{x^2}{2^2}+\frac{y^2}{(\sqrt2)^2}=1$$
This gives the correct parametrisation:
$$x=2\cos t\qquad y=\sqrt2\sin t\qquad t\in[0,2\pi]$$