If \( \mathrm{x}=\mathrm{a} \sec \theta \cos \phi, \mathrm{y}=\mathrm{b} \sec \theta \sin \phi \...

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