First slide

Equation of line in Straight lines

Question

$Area of quadrilateral formed by the lines 4 y - 3 x - a = 0, 3 y - 4 x + a = 0, 4 y - 3 x - 3 a = 0 and 3 y - 4 x + 2 a = 0 is$

Moderate

A

$\frac{a^{2}}{5}$
B

$\frac{a^{2}}{7}$
C

$\frac{2 a^{2}}{7}$
D

$\frac{2 a^{2}}{9}$

Solution

$The area of the parallelogram formed by the lines$
$\begin{array}{l} a_{1} x + b_{1} y + c_{1} = 0 \\ a_{2} x + b_{2} y + d_{1} = 0 \\ a_{1} x + b_{1} y + c_{2} = 0, \\ a_{2} x + b_{2} y + d_{2} = 0 is \\ |\frac{(c_{1} - c_{2}) (d_{1} - d_{2})}{a_{1} b_{2} - a_{2} b_{1}}| sq. units. \\ ∴ Required area = |\frac{(2 a) (a)}{(4) (- 4) - (3) (- 3)}| = \frac{2 a^{2}}{7} \end{array}$

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