A) \[\sqrt{\frac{17}{20}}\]
B) \[\sqrt{\frac{20}{17}}\]
C) \[\sqrt{\frac{3}{20}}\]
D) \[\sqrt{\frac{20}{3}}\]
Correct Answer: A
Solution :
If \[y=mx+c\] touches \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1,\] then \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}\]. Here \[c=6,\,\,{{a}^{2}}=100,\,\,{{b}^{2}}=49\] \[\therefore 36=100{{m}^{2}}-49\Rightarrow 100{{m}^{2}}=85\Rightarrow m=\sqrt{\frac{17}{20}}\].
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