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  • 1. a2 – b 2– c2 – 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

1. a2 – b 2– c2 – 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

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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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Deependra Verma

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