A) \[{{c}^{2}}={{a}^{2}}{{m}^{2}}+{{b}^{2}}\]
B) \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}\]
C) \[{{c}^{2}}={{b}^{2}}{{m}^{2}}-{{a}^{2}}\]
D) \[{{a}^{2}}={{b}^{2}}{{m}^{2}}+{{c}^{2}}\]
E) none of these
Correct Answer: B
Solution :
The line\[y=mx+c\]touches the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]if \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}.\]
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