If a variable chord of the hyperbola \( x^{2}-y^{2}=9 \) touches the parabola \( y^{2}=12 x \), ...

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If a variable chord of the hyperbola \( x^{2}-y^{2}=9 \) touches the parabola \( y^{2}=12 x \), then locus of middle points of these chords is expressed as \( x^{3}+\lambda_{1} x y^{2}+\lambda_{2} y^{2}=0\left(\lambda_{1}, \lambda_{2} \in \mathrm{I}\right) \), then:
(a) \( \lambda_{1}+\lambda_{2}=2 \)
(b) \( \lambda_{1}^{2}+\lambda_{2}^{2}=10 \)
(c) Number of divisors of \( \left(\lambda_{1}^{2}+\lambda_{2}^{2}\right) \) is 4
(d) Number of divisors of \( \left(\lambda_{1}^{2}+\lambda_{2}^{2}\right) \) is 6
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