A) \[\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}}=1\]
B) \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]
C) \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]
D) \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=0\]
Correct Answer: A
Solution :
| [a] We have, \[x=a\tan \theta \] and \[y=b\sec \theta \] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\tan \theta =\frac{x}{a}\] and \[\sec \theta =\frac{y}{b}\] |
| Putting these values in \[{{\sec }^{2}}\theta -{{\tan }^{2}}\theta =1,\] we get |
| \[\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}}=1\] |
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