Question

Area of the rhombus bounded by the four lines, $ax\pm by\pm c=0$ is

• A. $\frac{c^2}{2ab}$
• B. $\frac{2c^2}{ab}$
• C. $\frac{4c^2}{ab}$
• D. $\frac{ab}{4c^2}$

Answer 1

The correct option is B $\frac{2c^2}{ab}$

The four lines will form a rhombus. The coordinates of the vertices are $(-\frac{c}{a},0),(\frac{c}{a},0),(0,\frac{c}{b}),(0,-\frac{c}{b})$
Let $d_1,d_2$ be the diagonals of the rhombus.
$d_1=\frac{2c}{a}$
$d_2=\frac{2c}{b}$
Area$=\frac{1}{2}{d}_1.d_2$ $=\frac{2c^2}{ab}$