Category : JEE Main & Advanced
The equations \[x=a\sec \varphi \] and \[y=b\tan \varphi \] are known as the parametric equations of the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]. This \[(a\sec \varphi ,\,b\tan \varphi )\] lies on the hyperbola for all values of \[\varphi \].
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