Let 0 < a < b. Consider two circles with radii a and b and centers
(a, 0) and (b, 0) respectively with 0 < a < b. Let c be the center of any
circle in the crescent shaped region M between the two circles and
tangent to both (See figure below). Determine the locus of c as its
circle traverses through region M maintaining tangency.
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UP 0 DOWN 0 0 2
2 Answers
383This is the locus of an ellipse with foci at (a, 0) and (b, 0).
Tanumoy Bar Please explain it.Upvote·0· Reply ·2013-02-20 03:10:00
383join ac & bc
if the radius of the small circle is r then
ac=a+r
bc=b-r
ac+bc= a+b (constant)