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  4. Equation of diagonals of a rectangle with area 32 sq. units are y+2 x-4=0 and y-2 x-12= 0 , then equation(s) of its sides(s) is/are

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Q. Equation of diagonals of a rectangle with area $32 sq$. units are $y+2 x-4=0$ and $y-2 x-12=$ 0 , then equation(s) of its sides(s) is/are

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Solution:

$y + 2x - 4 = 0$
$y-2 x-12=0$
$y=8 \Rightarrow$ point of intersection of diagonals is $(-2,8)$ $x =-2$
$m _1+ m _2=-2+2=0$
angle bisectors are parallel to $x$-axis & $y$-axis.
image
$\tan \theta=\frac{b}{a}=2 \Rightarrow b=2 a $
$\text { also } \quad 4 a b=32$
$8 a^2=32 $
$\Rightarrow a=2, b=4$
$\therefore \text { Equation of sides are } x=0, x=-4, y=4, y=12$