Question

Find equations of lines containing the point A(3, 4) and making 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, 4).

∴ `3/"a" + 4/"b"` = 1  ...(ii)

Since, the required line make equal intercepts on the co-ordinate axes.

∴ a = b   ...(iii)

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

`3/"a" + 4/"a"` = 1

∴ `7/"a"` = 1

∴ a = 7

∴ b = 7   ...[From (iii)]

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

`x/7 + y/7` = 1

∴ x + y = 7

Case II: Line passing through origin.

Slope of line passing through origin and A(3, 4) is

m = `(4 - 0)/(3 - 0) = 4/3`

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

∴ The equation of the required line is y = `4/3x`

∴ 4x – 3y = 0