Question

The straight lines ax + by + c = 0, where 3a + 2b + 4c = 0 are concurrent at the point -

• A. (3/4, 1/2)
• B. (1/2, 3/4)
• C. (-3/4, -1/2)
• D. (-3/4, 1/2)

Answer 1

The correct option is A (3/4, 1/2)

$L_1:ax+by+c=0$

$L_2:3a+2b+4c=0$

$\text{For concurrent points, suppose}$

$\text{the two axes be a and b.}$

Now, take the ratio,

$\frac{x}{3}=\frac{y}{2}=\frac{c}{4c}$

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

Hence,

$(x,y)\equiv (\frac{3}{4},\frac{1}{2})$