A) \[(6,3)\]
B) \[(6,-3)\]
C) \[(6,-6)\]
D) \[(6,5)\]
Correct Answer: B
Solution :
Given equation of curve is \[3{{x}^{2}}-4{{y}^{2}}=72.\] Since, the points \[(6,3)\] and \[(6,-3)\] lies on the curve. At point \[(6,\,\,3)\] \[{{d}_{1}}=\frac{3(6)+2(-3)-1}{\sqrt{{{3}^{2}}+{{2}^{2}}}}=\frac{23}{\sqrt{13}}\] At point \[(6,-3)\] \[{{d}_{2}}=\frac{3(6)+2(-3)-1}{\sqrt{{{3}^{2}}+{{2}^{2}}}}=\frac{11}{\sqrt{13}}\] Here, \[{{d}_{2}}\] is maximum. Hence, the point \[(6,-3)\] is on the curve which is nearest to the given line.
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