A) 0
B) 1
C) 2
D) 4
Correct Answer: B
Solution :
[b] The length of perpendicular from \[P(2,-3)\] on the given family of lines \[=\frac{a(4-3+4)+b(2+6-3)}{\sqrt{{{(2a+b)}^{2}}+{{(a-2b)}^{2}}}}=\pm \sqrt{10}\] (Given) \[\Rightarrow 5a+5b=\pm \sqrt{10(5{{a}^{2}}+5{{b}^{2}})}\] \[\Rightarrow 25{{(a+b)}^{2}}=50({{a}^{2}}+{{b}^{2}})\] \[\Rightarrow 25{{(a-b)}^{2}}=0\Rightarrow a=b\] For which we get only line \[3x-y+1=0\]
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