Question

The figure formed by the lines ax ± by ± c = 0 is
(a) a rectangle
(b) a square
(c) a rhombus
(d) none of these

Answer 1

(c) 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, $AB=BC=CD=DA=\sqrt{\frac{a^2}{c^2}+\frac{b^2}{c^2}}=\frac{\sqrt{a^2+b^2}}{\left|c\right|}$

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