Question

Obtain the equation of the line passing through the intersection of lines 4x – 3y – 1 = 0 and 2x – 5y + 3 = 0 and equally inclined to the axes.

Answer 1

Given lines are

4x – 3y – 1 = 0 …(1)

2x – 5y + 3 = 0 …(2)

(1) – 2 × (2) ⇒ 7y – 7 = 0 ⇒ y = 1

Putting the value of y in equation (1)

We get x = 1

∴ (1, 1) is the point of the line which is equally inclined to the axes be

\(\frac{x}{a}\) + \(\frac{y}{a}\) = 1

⇒ x + y = a …(3)

Since (3) passes through (1, 1)

∴ (3) ⇒ a = 2

∴ Equation of the line is

x + y – 2 = 0