If \( x=a \sec \theta \cos \phi, y=b \sec \theta \sin \phi \) and \( z=c \tan \theta \), then \(...

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If \( x=a \sec \theta \cos \phi, y=b \sec \theta \sin \phi \) and \( z=c \tan \theta \), then \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= \)
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(a) \( \frac{z^{2}}{c^{2}} \)
(b) \( 1-\frac{z^{2}}{c^{2}} \)
(c) \( \frac{z^{2}}{c^{2}}-1 \)
(d) \( 1+\frac{z^{2}}{c^{2}} \)
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