Question

The area (in square units) of the quadrilateral formed by the two pairs of lines

$l^2{x}^2-m^2{y}^2-n(lx+my)=0$

and $l^2{x}^2-m^2{y}^2+n(lx-my)=0$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given lines are (on factorising)

lx + my = 0, lx - my + n = 0

lx - my = 0, lx + my - n = 0

Area = $\left|\frac{(c_1-d_1)(c_2-d_2)}{(a_1{b}_2-a_2{b}_1)}\right|=\left|\frac{(0-n)(0+n)}{(-lm-lm)}\right|=\frac{n^2}{2|lm|}$.