Compute the radius of the largest circle that is internally tangent to the ellipse at $(3,0),$ and intersects the ellipse only at $(3,0).$

radius of the largest circle is Zero.

Step-by-step explanation: A circle can't fit into an ellipse with such coordinate (3,0). What that coordinate means is that the ellipse lies along the x axis 3unit from the origin along the x axis and 0 unit from the origin along the y axis. At which no circle can fit in.

Moreso, the the coordinates at which the circle intercepts the ellipse as to be uniform not (3,0).

A circle as a constant radii coordinate on both axis.

I believe you can now see why my answer is Zero.

step-by-step explanation: