Tangent are drawn from any point on the hyperbola \( x^{2} / 9- \) \( y^{2} / 4=1 \) to the circ...

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Tangent are drawn from any point on the hyperbola \( x^{2} / 9- \) \( y^{2} / 4=1 \) to the circle \( x^{2}+y^{2}=9 \). If the locus of the mid-point of the chord of contact is a \( a\left(x^{2}+y^{2}\right)^{2}=b x^{2}-c y^{2} \), then the value of \( a^{2}+b^{2}+c^{2}-7870 \) is equal to
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