If the roots of the equation \[ \left(x_{1}^{2}-a^{2}\right) m^{2}-...

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If the roots of the equation
\[
\left(x_{1}^{2}-a^{2}\right) m^{2}-2 x_{1} y_{1} m+y_{1}^{2}+b^{2}=0(ab)
\]
\( \mathrm{P} \)
are the slopes of two perpendicular lines intersecting at
W \( P\left(x_{1}, y_{1}\right) \), then the locus of \( P \) is
(1) \( x^{2}+y^{2}=a^{2}+b^{2} \)
(2) \( x^{2}+y^{2}=a^{2}-b^{2} \)
(3) \( x^{2}-y^{2}=a^{2}+b^{2} \)
(4) \( x^{2}-y^{2}=a^{2}-b^{2} \)
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