Question

An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as a center, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. Compute the radius of the circle.

Answer 1

2

Explanation:

The distance between foci is the root of the difference of the squares of the axes lengths:

d = √(10² -8²) = √36 = 6

Then the radius of the circle is half the difference between this and the length of the major axis:

r = (10 -6)/2 = 4/2

r = 2