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Tangents to the ellipse \( b^{2} x^{2}+a^{2} y^{2}=a^{2} b^{2} \) make
\( \mathrm{P}^{11:} \) angles \( \alpha \) and \( \beta \) with the major axis such that

W \( \tan \alpha+\tan \beta=\lambda \). The locus of their point of intersection is
(1) \( x^{2}+y^{2}=a^{2} \)
(2) \( x^{2}+y^{2}=b^{2} \)
(3) \( x^{2}-a^{2}=2 \lambda x y \)
(4) \( \lambda\left(x^{2}-a^{2}\right)=2 x y \)
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