SOLUTION: One circle is internally tangent to an ellipse with the equation {{{ 4x^2 + 9y^2 =36 }}}. Another circle is externally tangent to the same ellipse. Write the equations of the 2 cir

Question 1034719: One circle is internally tangent to an ellipse with the equation . Another circle is externally tangent to the same ellipse. Write the equations of the 2 circles if all 3 graphs have the same center.
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Well, the center of the ellipse is the origin...that makes life easier...thus the two circles we are interested in are also centered on the origin...
If we put the ellipse in standard form, we get

This tells us the semi-major axis is 3 and the semi-minor axis is 2.
These correspond to the radii of the inscribed and circumscribed circles.
Draw them and see for yourself.
Their equations are then

and

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