As shown in the figure, the circle is moving upwards along the line $x=x_0$
suppose we know the following parameters: $a,b,x_0,r$
The ellipse equation is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$;
The circle equation is $(x-x_0)^2+(y-y_0)^2=r^2$
how to find the tangent point and the $y_0$