There is an ellipse that is parameterized as
x[t] = 4 Cos[t];
y[t] = 2 Sin[t];
P[t] = {x[t],y[t]};
And we are given a drill bit that is r inches in radius. We are instructed to find the largest radius drill bit that will exactly cut out the ellipse without taking any area outside of the ellipse.
The above image details the following: The black circle is the drill bit that is used to cut out the Blue colored ellipse. The red elliptic path is the path the center of the drill bit has to move in-order to cutout the ellipse. The blue ellipse is the shape to be cut out.
The radius of the black circle is 2.35 and it just about cuts out the blue ellipse.
The above image arises when a drill bit of diameter 3.35 is used. Note that the drill bit takes out areas that are beyond the blue ellipse.
How can I figure out the largest drill bit that would exactly cut out the ellipse with out removing any area beyond the ellipse? What would be the understanding or methodology to identify that max radius?