Write the area of the figure formed by the lines `a|x|+b|y|+c=0.`

Options

A. `(c^(2))/(|ab|)`
B. `(2c^(2))/(|ab|)`
C. `(c^(2))/(2|ab|)`
D. none of these

Answer

B

Explanation

We have , `a|x|+b|y|+c=0`
This is equivalent to the following system of equations:
`ax+by+c=0" "ax+by+c=0`
`-ax-by+c=0` or, `ax+by-c=0`
`ax-by+c=0" "ax-by+c=0`
`-ax+by+c=0" "ax-by-c=0`
These lines from a parallelogram whose area A is given by
`A=|({c-(-c)}{c-(-c)})/(|{:(a,a),(b,-b):}|)|=(4c^(2))/(2|ab|)=(2c^(2))/(|ab|)`
ALITER Given equations form a rhombus as shown in Fig. 15.
`therefore ` Required area `=(1)/(2)(PRxxQS)=(1)/(2)|(2c)/(a)|xx|(2c)/(b)|=(2c^(2))/(|ab|)`