Question

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

• A. $(\frac{3}{4},\frac{1}{2})$
• B. $(\frac{1}{2},\frac{1}{2})$
• C. $(0,10)$
• D. $\left(1.1\right)$

Answer 1

The correct option is A $(\frac{3}{4},\frac{1}{2})$

$3a+2b+4c=0$

$\frac{3}{4}a+\frac{2}{4}a+c=0$

$\frac{3}{4}a+\frac{b}{2}+c=\mathrm{0......}\left(1\right)$

Now $ax+by+z=\mathrm{0....}\left(2\right)$

from (1) and (2)

$x=\frac{3}{4};y=\frac{1}{2}$

Cncurrent at $\equiv (\frac{3}{4},\frac{1}{2})$