A) \[c=10\]
B) \[{{c}^{2}}=80\]
C) \[c=12\]
D) \[{{c}^{2}}=64\]
Correct Answer: B
Solution :
If \[y=mx+c\] touches the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\], then \[{{c}^{2}}={{a}^{2}}=(1+{{m}^{2}})\] Now the line \[y=2x+c\] touches me circle \[{{x}^{2}}+{{y}^{2}}=16\]if \[\therefore \] \[{{c}^{2}}=16\,\,(1+4)=16\times 5\] or \[{{c}^{2}}=80\]
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