The area of a parallelogram formed by the lines `a x+-b x+-c=0` is (a) `(c^2)/((a b))` (b) `(2 c^2)/((a b))` (c) `(c^2)/(2a b)` (d) none of these

Options

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

Answer

B

Explanation

The given lines are
`ax+-by+-c=0`
`"or " (x)/(+-c//a) +(y)/(+-c//b)=1`
The vertices of rhombus are at A(c/a,0), C(-c/a,0), B(0,c/b), D(0,-c/b). Therefore, the diagonals AC and BD of quadrilateral ABCD are perpendicular. Hence, it is a rhombus whose are is given by
`(1)/(2) xx AC xx BD = (1)/(2) xx (2c)/(b) xx (2c)/(b) = (2c^(2))/(ab)`