Question

The figure formed by the lines $ax\pm by\pm c=0$ is

• A. a rectangle
• B. a square
• C. a rhombus
• D. none of these

Answer 1

The correct option is C

a rhombus

The given lines can be written separately in the following manner :

$ax+by+c=0...\left(1\right)$

$ax+by-c=0...\left(2\right)$

$ax-by+c=0...\left(3\right)$

$ax-by-c=0...\left(4\right)$

Graph of the given lines is given below:

Dlearly, 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.