Ellipses and Circles!

Geometry Level 3

An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as the center, a circle is drawn that is tangent to the ellipse, with not part of the circle being outside the ellipse. Compute the radius of the circle.


The answer is 2.

Walid Mustafa by Walid Mustafa , 22, Ireland

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2 solutions

Ajit Athle
Feb 2, 2015

We've: x²/25+y²/16=1 and (x-3)²+y²=r². Solve for y in terms of r and set y=0 to obtain r² -10r +16 = 0 which gives r=2 or 8 of which the former is the admissible solution.

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Guru Prasaadh
Apr 5, 2015

first of all i would say this should be a 20 points problem. as the eccentricity is 3/5 therefore the focus is (3,0) or (-3,0). now its tangent to the ellipse . draw the diagram you will have to just count the difference between the endpoint of major axis and the focus.

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