Question

The figure formed by the lines ax ± by ± c = 0 is

Options

• a rectangle

• a square

• a rhombus

•  none of these

Answer 1

a rhombus

The given lines can be written separately in the following manner:
ax + by + c = 0       ... (1)
ax + by − c = 0       ... (2)
ax − by − c = 0       ... (3)
ax − by − c = 0       ... (4)
Graph of the given lines is given below:

Clearly,

\[\text { AB = BC = CD = DA} = \sqrt{\frac{a^2}{c^2} + \frac{b^2}{c^2}} = \frac{\sqrt{a^2 + b^2}}{\left| c \right|}\]

Thus, the region formed by the given lines is ABCD, which is a rhombus.