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Tangents to the hyperbola (x^(2))/(a^(2)...

Tangents to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` make angle `theta_(1), theta_(2)` with transvrse axis of a hyperbola. Show that the points of intersection of these tangents lies on the curve `2xy=k(x^(2)-a^(2))` when `tan theta_(1)+ tan theta_(2)=k`

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