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The exhaustive set of values of alpha^2 ...

The exhaustive set of values of `alpha^2` such that there exists a tangent to the ellipse `x^2+alpha^2y^2=alpha^2` and the portion of the tangent intercepted by the hyperbola `alpha^2x^2-y^2=1` subtends a right angle at the center of the curves is:

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To solve the problem, we need to find the exhaustive set of values of \( \alpha^2 \) such that there exists a tangent to the ellipse \( x^2 + \alpha^2 y^2 = \alpha^2 \) and the portion of the tangent intercepted by the hyperbola \( \alpha^2 x^2 - y^2 = 1 \) subtends a right angle at the center of the curves. ### Step 1: Write the equations of the curves The given ellipse can be rewritten as: \[ \frac{x^2}{\alpha^2} + \frac{y^2}{1} = 1 \] The given hyperbola is: ...
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