Question

Answer the following question:

Find the equation of the line which contains the point A(3, 5) and makes equal intercepts on the co-ordinates axes.

Answer 1

Case I: Line not passing through the origin.

Let the equation of the line be `x/"a" + y/"b"` = 1 ...(i)

This line passes through A(3, 5).

∴ `3/"a" + 5/"b"` = 1 ...(ii)

Since the required line makes equal intercepts on the co-ordinates axes,

a = b ...(iii)

Substituting the value of b in (ii), we get

`3/"a" + 5/"a"` = 1

∴ `8/"a"` = 1

∴ a = 8

∴ b = 8 …[From (iii)]

Substituting the values of a and b in equation (i), the equation of the required line is

`x/8 + y/8` = 1

∴ x + y = 8

Case II: Line passing through the origin.

Slope of line passing through origin and

A(3, 5) is m = `(5 - 0)/(3 - 0) = 5/3`

∴ Equation of the line having slope m and passing through the origin (0, 0) is y = mx.

∴ The equation of the required line is

y = `5/3x`

∴ 5x – 3y = 0