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प्रश्न
The figure formed by the lines ax ± by ± c = 0 is
विकल्प
a rectangle
a square
a rhombus
none of these
उत्तर
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.
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