Check if disk lies within an ellipse I have an ellipse in normal form centered at the origin and want to check whether a disk with given center point and radius is contained completely in the ellipse without touching it.

If I could compute the shortest distance between a point and the ellipse then I can just check if this distance is larger than the disk radius. How would I calculate this distance and are there other ways to solve this problem?

(Related to this question.)
Supposing that the disk's equation is given by:

$$(x-x_0)^2 + (y-y_0)^2 \le r^2 \ \ \ (\star)$$

And that the interior of the ellipse has the equation:

$$\frac{(x-x_1)^2}{a^2} + \frac{(y-y_1)^2}{b^2} &lt; 1 \ \ \ (\star \star)$$

Check whether $(\star) \implies (\star \star)$
Disk equation is given by:

$$(x-h)^2 + (y-k)^2= R^2 $$

And ellipse :

$$\frac{(x-H)^2}{a^2} + \frac{(y-K)^2}{b^2}= 1 \ \ \  $$

Calculate a value of x or y intersection after eliminating one of them.

To be within the ellipse the quadratic equation should have imaginary roots, discriminant should be $&lt;0$ or zero for contacting ellipse and circle.