ellipse boundary after rotation Assume I have this vertical ellipse with a certain major axis $a$ and minor axis $b$.

If we take the center of the ellipse to be at $(0,0)$, then the top right small red circle will be at $(b,a)$.
Then I rotate it (say by an arbitrary angle $\theta$) about its center:

My question is this: what is the new position of the top right small red circle in this new image after rotation relative to the fixed center? For example at $\theta=90^\circ$ its position will be $(a,b)$.

Following Pocho la pantera's explanation, I just thought to extend it. We know that for the rotated ellipse: 
$$
x=acos(t)cos(\theta)+bsin(t)sin(\theta)
$$
Taking the derivative and setting it to zero we find the $t$ that gives the extremuems of x:
$$
\frac{dx}{dt}=-asin(t)cos(\theta)+bcos(t)sin(\theta)=0
$$
$$
asin(t)cos(\theta)=bcos(t)sin(\theta)
$$
$$
tan(t)=\frac{b}{a}tan(\theta)
$$
Following the same steps for $y$ we find the $t$ that gives the maximum $y$:
$$
y=-acos(t)sin(\theta) + bsin(t)cos(\theta)
$$
$$
\frac{dy}{dt}=asin(t)sin(\theta)+bcos(t)cos(\theta)=0
$$
$$
asin(t)sin(\theta)=-bcos(t)cos(\theta)
$$
$$
tan(t)=-\frac{b}{a}cot(\theta)
$$
