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

Open in App
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, $AB=BC=CD=DA=\sqrt{\frac{{a}^{2}}{{c}^{2}}+\frac{{b}^{2}}{{c}^{2}}}=\frac{\sqrt{{a}^{2}+{b}^{2}}}{\left|c\right|}$ Thus, the region formed by the given lines is ABCD, which is a rhombus.

Suggest Corrections
0
Related Videos
Limits Tending to Infinity and Sequential Limits
MATHEMATICS
Watch in App