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

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Solution

(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, $A B = B C = C D = D A = \sqrt{\frac{a^{2}}{c^{2}} + \frac{b^{2}}{c^{2}}} = \frac{\sqrt{a^{2} + b^{2}}}{|c|}$

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

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