Question

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

• A. $\frac{2c^2}{\left|\begin{array}{c}ab\end{array}\right|}$
• B. $\frac{4c^2}{\left|\begin{array}{c}ab\end{array}\right|}$
• C. $\frac{\left|\begin{array}{c}ab\end{array}\right|}{4c^2}$
• D. $\frac{c^2}{\left|\begin{array}{c}ab\end{array}\right|}$

Answer 1

The correct option is A $\frac{2c^2}{\left|\begin{array}{c}ab\end{array}\right|}$

Area of $DOAB=\left|\begin{array}{c}\frac{1}{2},\frac{c}{a},\frac{c}{b}\end{array}\right|=\frac{1}{2}\frac{c^2}{\left|\begin{array}{c}ab\end{array}\right|}$

Area of the rhombus $=4.\frac{1}{2}\frac{c^2}{\left|\begin{array}{c}ab\end{array}\right|}=\frac{2c^2}{\left|\begin{array}{c}ab\end{array}\right|}$