if 2a+b+2c=0, then the family of lines ax+by+c=0 is concurrent at??
From 2a+b+2c=0
c = -(2a + b)/2 ..........................................(1)
Put (1) in ax+by+c=0
=> ax+by - a - b/2 = 0
=> a(x-1) + b(y - 1/2) = 0
{ comparing coefficients to zero we get,
a(x-1) = 0 or x = 1
and
b(y - 1/2) = 0 or y = 1/2
Hence family of lines ax+by+c=0 is concurrent at (1,1/2)
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