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A line through the origin meets the circle \( x^{2}+y^{2}=a^{2} \) at \( P \& \) the hyperbola \( x^{2}-y^{2}=a^{2} \) at Q. If the locus of the point of intersection of the tangent at \( \mathrm{P} \) to the circle and the tangent at \( \mathrm{Q} \) to the hyperbola is the curve \( a^{4}\left(x^{2}-a^{2}\right)+\lambda x^{2} y^{4}=0 \), then find the value of \( \lambda \).
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