Intersection of a Line and a Hyperbola
Category : JEE Main & Advanced
The straight line \[y=mx+c\] will cut the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] in two points may be real, coincident or imaginary according as \[{{c}^{2}}>,\,=,\,<{{a}^{2}}{{m}^{2}}-{{b}^{2}}\].
Condition of tangency : If straight line \[y=mx+c\] touches the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}\].
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