# 1. a2 â€“ b 2â€“ c2 â€“ 2bc = 0 , then the family of lines ax + by + c = 0 are concurrent at the points: a. (0,1) b. (1,-1) c. (-1,1) d. none of the above

$a^2-b^2-c^2 -2bc=0\\* \Rightarrow a^2=b^2+c^2+2bc\\*\Rightarrow a^2=(b+c)^2\\* \Rightarrow a=b+c\\* \Rightarrow a-b=c\\* ax+by+c=0 \\* Now,\;put\;c=a-b\\* ax+by+a-b=0\\*\Rightarrow ax+a+by-b=0 \\* a(x+1)+b(y-1)=0\\* \Rightarrow x+1=0\;and\;y-1=0\\* \Rightarrow x=-1\;and\;y=1\\*\Rightarrow (-1,1)$

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