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Locus of perpendicular from center upon normal to
P the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) is

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(1) \( \left(x^{2}+y^{2}\right)^{2}\left(\frac{a^{2}}{x^{2}}+\frac{b^{2}}{y^{2}}\right)=\left(a^{2}-b^{2}\right)^{2} \)
(2) \( \left(x^{2}+y^{2}\right)^{2}\left(\frac{a^{2}}{x^{2}}-\frac{b^{2}}{y^{2}}\right)=\left(a^{2}+b^{2}\right)^{2} \)
(3) \( \left(x^{2}+y^{2}\right)^{2}\left(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}\right)=\left(a^{2}+b^{2}\right)^{2} \)
(4) None of these
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