Question: The graph shows two red circles with centers (1, 0) and (1, 0) and radii 3 and 5, respectively. Consider the collection of all circles

The graph shows two red circles with centers (–1, 0) and (1, 0) and radii 3 and 5, respectively. Consider the collection of all circles tangent to both of these circles. (Some of these are shown in blue.) Show that the centers of all such circles lie on an ellipse with foci (±1, 0). Find an equation of this ellipse.

T y 1 0 1 X

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