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An ellipse and a hyperbola are confocal ...

An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse. If `e_1a n de_2` are the eccentricities of the ellipse and the hyperbola, respectively, then prove that `1/(e1 2)+1/(e2 2)=2` .

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To solve the problem, we will follow these steps: ### Step 1: Define the parameters of the ellipse and hyperbola Let: - The semi-major axis of the ellipse be \( a_1 \) - The semi-minor axis of the ellipse be \( b_1 \) - The eccentricity of the ellipse be \( e_1 \) - The semi-major axis of the hyperbola be \( a_2 \) ...
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