A) 1
B) 2
C) 4
D) Infinitely many
Correct Answer: B
Solution :
The equation of any line parallel to \[2x+6y+7=0\]is\[2x+6y+k=0\]. This meets the axes at \[A\left( -\frac{k}{2},0 \right)\]and\[B\left( 0,-\frac{k}{6} \right)\]. By hypothesis, \[AB=10\] \[\Rightarrow \sqrt{\frac{{{k}^{2}}}{4}+\frac{{{k}^{2}}}{36}}=10\Rightarrow \sqrt{\frac{10{{k}^{2}}}{36}}=10\] Þ \[10{{k}^{2}}=3600\Rightarrow k=\pm 6\sqrt{10}\]. Hence there are two lines given by\[2x+6y\pm 6\sqrt{10}=0\].
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