Tangents are drawn from any point on the hyperbola \( 4 x^{2}-9 y^{2}=36 \) to the circle \( x^{...

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Tangents are drawn from any point on the hyperbola \( 4 x^{2}-9 y^{2}=36 \) to the circle \( x^{2}+y^{2}-9=0 \).
The locus of mid-point of chord of contact is \( \left(\frac{\mathrm{x}^{2}}{9}-\frac{\mathrm{y}^{2}}{4}\right)=\left(\frac{\mathrm{x}^{2}+\mathrm{y}^{2}}{\mathrm{k}}\right)^{2} \), where \( k \in N \). Find \( k \).
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