# A Problem on Conics!

Geometry Level 5

What is the exhaustive set of values of $$\displaystyle \alpha^2$$ such that there exists a tangent to the ellipse $$\displaystyle x^2+\alpha^2y^2=1$$ and the portion of tangent intercepted by hyperbola $$\displaystyle x^2-\alpha^2y^2=1$$ subtends a right angle at the centre of the curves?

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