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Two circles of radius $r$ are externally tangent to each other and internally tangent to the ellipse $x^2 + 5y^2 = 6,$ as shown below. Find $r.$

 Dec 28, 2020
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The equation of the circle is (x - r)^2 + y^2 = r^2

==> 2(x - r) + 2y*y' = 0

 

The equation of the ellipse is x^2 + 5y^2 = 6

==> 2x + 10y*y' = 0

 

Matching the derivatives, we get r = 4/5.

 Dec 31, 2020

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