First slide

Equation of line in Straight lines

Question

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

Very Easy

A

(4, 3)
B

(1/4, 1/3)
C

(1/2,1/3)
D

None of these

Solution

The set of lines is 4ax + 3by + c = 0, where a + b + c = 0.
Eliminating c, we get
$\begin{aligned} 4 a x + 3 b y - (a + b) = 0 \\ or a (4 x - 1) + b (3 y - 1) = 0 \end{aligned}$
This passes through the intersection of the lines 4x - 1 = 0
$and 3 y - 1 = 0, i.e., x = 1 / 4, y = 1 / 3, i.e., (1 / 4, 1 / 3) .$

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