Question

The point of concurrence of the line $ax+by+c=0$ and $a,b,c$ satisfy the relation $3a+2b+4c=0$ is

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

Answer 1

The correct option is C

$\left(\frac{3}{4},\frac{1}{2}\right)$

Explanation for the correct option:

Find the required points.

Given relation: $3a+2b+4c=0$

Divide both sides by $4$

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

The equation of the given line is: $ax+by+c=0$

Comparing the above equation with equation $\left(1\right)$, we get

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

So, the required point is $\left(\frac{3}{4},\frac{1}{2}\right)$

Hence, option (C) is the correct answer.