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Let \( P(a \sec \theta, b \tan \theta) \) and \( Q(a \sec \varphi, b \tan \varphi) \),
\( \mathrm{P} \) where \( \theta+\varphi=\frac{\pi}{2} \), be two points on the hyperbola

W \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \). If \( (h, k) \) is the point of intersection of the normals at \( P \) and \( Q \), then \( k \) is equal to
(1) \( \frac{a^{2}+b^{2}}{a} \)
(2) \( -\left(\frac{a^{2}+b^{2}}{a}\right) \)
(3) \( \frac{a^{2}+b^{2}}{b} \)
(4) \( -\left(\frac{a^{2}+b^{2}}{b}\right) \)
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