A geometry problem by ashwin korade

Geometry Level 3

if the eccentricity of the hyperbola \(x^2-y^2 \sec^2 \alpha = 5\) is \(\sqrt{3}\) times eccentricity of the ellipse \(x^2 \sec^2 \alpha + y^2 = 25\), then find the value of \(\alpha\).

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