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If radii of director circle of the ellip...

If radii of director circle of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` and hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` are in the ratio `1:3 and 4e_(1)^(2)-e_(2)^(2)=lambda`, where `e_1 and e_2` are the eccetricities of ellipse and hyperbola respectively, then the value of `lambda` is

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`(7)`
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