First slide

Equation of line in Straight lines

Question

Given the system of straight line a(2x + y – 3) + b(3x + 2y – 5) = 0, the line of the system farthest form the point (4, –3) has the equation

Moderate

A

3x – 4y + 1 = 0
B

4x + 3y – 5 = 0
C

7x – y + 4 = 0
D

none of these

Solution

The given system of lines pass through (1, 1)
So, the required line is the through (1, 1) and perpendicular
to the join of (1, 1) and (4, –3).
$∴$ The equation of line is $\frac{y - 1}{x - 1} = \frac{3}{4}, i e ., 3 x - 4 y + 1 = 0$

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