Lets say I have an ellipse. Starting from the center of that ellipse is there a way I could find a vector (line segment) that when "rotated" around the initial point of the vector, the end point will always touch the circumference? if there is a way?
Edit: for clarity I'll explain my question better. First, I have draw an ellipse. it can be of any configuration. Next I draw a point from within anywhere in the ellipse's circumference. Now comes the part I need help with. Is there a equation/algorithm anything that allows me, knowing the parameters of my ellipse, to draw a line from wherever I place my point from within the ellipse to the exact edge of said ellipse. The idea why I said "rotation" was because I envisioned the line being drawn as a function of time, so whatever "t" value of time with put in our function. we would get a corresponding coordinate value for the edge of the circumference.
(see figure for clarity). 
If the ellipse origin is in $(0, 0)$ and the ellipse passes by points $(a, 0), (0, b), (-a, 0), (0, -b)$, a parametric equation is, for $\theta$ in $[0, 2\pi[$:
$x = a \cos \theta$
$y = b \sin \theta$
Then, the vector $v$ between a point $(x_0, y_0)$ and this point $(x, y)$ has coordinates:
$v_x = a \cos \theta - x_0$
$v_y = b \sin \theta - y_0$
(As remarked by @Intelligentipauca, please note that $\theta$ is not the angle made by the vector with the $x$ axis, even when the vector origin point is $(0, 0)$. It is this angle for a circle, i.e. an ellipse with $a=b$. On an ellipse you can find back this angle by "stretching the ellipse to a circle", i.e. vertically projecting the ellipse point onto a circle with radius $a$ and same center).