Question

Answer the following question:

Show that there are two lines which pass through A(3, 4) and the sum of whose intercepts is zero.

Answer 1

Case I: Line not passing through origin.

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

This line passes through (3, 4)

∴ `3/"a" + 4/"b"` = 1  ...(ii)

Since the sum of the intercepts of the line is zero,

a + b = 0

∴ a = – b  ...(iii)

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

`3/(-"b") + 4/"b"` = 1

∴ `1/"b"` = 1

∴ b  = 1

∴ a = – 1  ...[From (iii)]

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

`x/(-1) + y/1` = 1

∴ x – y = – 1

∴ x – y + 1 = 0

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

∴ There are two lines which pass through A(3, 4) and the sum of whose intercepts is zero.