Question

The set of lines $ax+by+c=0$, where $3a+2b+4c=0$ is concurrent at the point... .

Answer 1

The set of lines $ax+by+c=0$, where $3a+25+4c=0$ or $\frac{3}{4}a+\frac{1}{2}b+c=0$ are concurrent at $(x=\frac{3}{4},y=\frac{1}{2})i.e.$
comparing the coefficients of $x$ and $y$.
Thus, point of concurrency is $(\frac{3}{4},\frac{1}{2}).$
Alternate Solution
As, $ax+by+c=0$, satisfy $3a+26+4c=0$ which represents system of concurrent lines whose point of concurrency could be obtained by comparison as,
$ax+by+c\equiv \frac{3a}{4}+\frac{2}{4}b+c$
$\Rightarrow x=\frac{3}{4},y=\frac{1}{2}$ is point of concurrency.
$\therefore (\frac{3}{4},\frac{1}{2})$ is the required point.