I have a unit circle centered at the origin defined parametrically as $ x = \cos \ t,\ y = \sin \ t $ and an ellipse centered at the origin defined parametrically as $ x = a\cdot \cos \ t^\prime,\ y = b\cdot \sin \ t^\prime $ I need to find a formula to convert from $t$ to $t^\prime$.
I want to be able to draw an arc on the circle given $t_1$ and $t_2$ and draw the corresponding arc (using $t^\prime_1$ and $t^\prime_2$) on the ellipse so that I can draw a straight line from the origin that touches an endpoint of the arc on the circle and the corresponding endpoint on the ellipse.