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The tangents to \( y^{2}=4 a x \) make angles \( \theta_{1}, \theta_{2} \) with \( x \)-axis. If \( \cos \theta_{1} \cos \theta_{2}=\lambda \) then the locus of their point of intersection is
(A) \( x^{2}=\lambda^{2}\left[(x-a)^{2}+y^{2}\right] \)
(B) \( x^{2}=\lambda^{2}\left[(x+a)^{2}+y^{2}\right] \)
(C) \( x^{2}=\lambda^{2}\left[(x-a)^{2}+4 y^{2}\right] \)
(D) \( 4 x^{2}=\lambda^{2}\left[(x+a)^{2}+y^{2}\right] \)
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