Question

Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.

Answer 1

4x + 7y = 3       ..…(i)

2x – 3y = –1      .....(ii)

On multiplying equation (ii) by 2,

4x – 6y = – 2      ..…(iii)

By subtracting equation (iii) from (i)

13y = 5

∴ y = `5/13`

Putting the value of y in equation (i),

`4"x" + 7 xx 5/13 = 3`

or `4"x" = 3 - 35/13`

= `(39 - 35)/13`

= `4/13`

∴ `"x" = 1/13`

The given lines intersect at the point `(1/3, 5/13)`.

Lines whose intercepts on the axes are equal make an angle of 45° or 135° with the positive x-axis. Therefore its slope will be ±1.

∴ Equations of lines PA and PB

y – y₁ = m(x – x₁)

(i) When m = 1, then y – `5/13 = 1 ("x" - 1/13)`

or 13y – 5 = 13 x – 1 or 13x – 13y + 4 = 0

(ii) When m = –1, then y – `5/13 = 1 ("x" - 1/3)`

13y – 5 = –13x + 1

∴ 13x + 13y – 6 = 0