First slide

Equation of line in Straight lines

Question

The area of a parallelogram formed by the lines $ax \pm by \pm c = 0$ is

Moderate

A

$c^{2} / (ab)$
B

$2 c^{2} / (ab)$
C

$c^{2} / 2 ab$
D

none of these

Solution

The given lines are $ax \pm by \pm c = 0$
or $\frac{x}{\pm c / a} + \frac{y}{\pm c / b} = 1$
The vertices of rhombus are are $A (c / a, 0), C (- c / a, 0)$ , $B (0, c / b), D (0, - c / b) .$ Therefore the diagonal AC and BD of quadrilateral $ABCD$ are perpendicular. Hence, it is a rhombus whose area is given by
$\frac{1}{2} \times A C \times B D = \frac{1}{2} \times \frac{2 c}{a} \times \frac{2 c}{b} = \frac{2 c^{2}}{a b}$

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