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From any point on the hyperbola $x^{2} - y^{2} = a^{2} - b^{2}$ two tangent are drawn to the ellipse $x^{2} / a^{^{2}} + y^{2} / b^{2} = 1 .$ Then they make angles $α a n d β$ such that

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$\tan α - \tan β = 1$

$\tan α \tan β = - 1$

$\tan α + \tan β = 1$

$\tan α \tan β = 1$

answer is C.

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Using $y = m x \pm \sqrt{a^{2} m^{2} + b^{2}}$

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