Position of a Point With Respect to a Hyperbola
Category : JEE Main & Advanced
Let the hyperbola be \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\].
Then \[P({{x}_{1}},\,{{y}_{1}})\] will lie inside, on or outside the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] according as \[\frac{x_{1}^{2}}{{{a}^{2}}}-\frac{y_{1}^{2}}{{{b}^{2}}}-1\] is positive, zero or negative.
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