Question

The 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

$\frac{2c^2}{ab}$

Correct option: (b)$\frac{2c^2}{ab}$

The given four lines, $ax\pm by\pm c=0$

The four lines will form a rhombus.

The coordinates of the vertices are

$\left(\frac{-c}{a},0\right),\left(\frac{-c}{a},0\right),\left(0,\frac{c}{b}\right),\left(0,\frac{-c}{b}\right)$

Let $d_1$ and $d_2$be the diagonals of the rhombus.

Then,

$$\begin{gathered} d_1=\frac{2c}{a} \\ {d}_2=\frac{2c}{b} \end{gathered}$$

Area of the rhombus$=\frac{1}{2}\times d_1\times d_2$

$$\begin{gathered} =\frac{1}{2}\times \frac{2c}{a}\times \frac{2c}{b} \\ =\frac{2c^2}{ab} \end{gathered}$$

Thus, area of rhombus is $\frac{2c^2}{ab}$

Hence, the correct option is (d )