Question

For all values of $a,b,c\in R$, the lines $ax+by+c=0$ are concurrent at

Answer 1

$ax+by+c=0$ ...(1)
For concurrency point will satisfy equation (1)
A) For point $(\frac{3}{4},\frac{1}{2})$
$a\frac{3}{4}+b\frac{1}{2}+c=0\Rightarrow 3a+2b+4c=0$
B) For point $(-2,-3)$
$a(-2)+b(-3)+c=0\Rightarrow 2a+3b-c=0$
C) For point $(\frac{5}{3},-\frac{4}{3})$
$a\frac{5}{3}-b\frac{4}{3}+c=0\Rightarrow 5a-4b+3c=0$
D) For point $(0,0)$
$a0+b0+c=0\Rightarrow c=0$