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jmc

algebra intermediate

Problem

An ellipse whose axes are parallel to the coordinate axes is tangent to the -axis at and tangent to the -axis at Find the distance between the foci of the ellipse.
Solution
The ellipse must have its center at the point Because is further from than it is from the major axis must lie parallel to the -axis and have length and so the minor axis lies parallel to the -axis and has length Therefore, the distance between the foci of the ellipse is
Final answer
2\sqrt{15}