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The ellipse E:(x^(2))/(25)+(y^(2))/(16)=...

The ellipse `E:(x^(2))/(25)+(y^(2))/(16)=1` is inscribed in a rectangle `R` whose sides are parallel to the coordinate axes. A hyperbola (with same centre and transverse axis same as major axis of ellipse) intersects the ellipse orthogonally and passes through the vertices of the rectangle.Then eccentricity of the hyperbola is

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