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The line y=x intersects the hyperbola x^...

The line `y=x` intersects the hyperbola `x^2/9-y^2/25=1` at the points `P and Q.` The eccentricity of ellipse with `PQ` axis and minor axis of length `5/sqrt2` is (A) `(sqrt 5)/3` (B) `5/(sqrt 3)` (C) `(2(sqrt 2))/3` (D) `3/(sqrt 2)`

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