Four sides of a quadrilateral are given by the equation xy (x-2) (y-3) = 0, then the equation of the line parallel to x – 4y = 0 that divides the quadrilateral into two equal parts is

Given sides xy ( x- 2) (y – 3) = 0

x = 0, y = 0, x - 2 = 0, y – 3 = 0

Area of rectangle = 2 x 3 = 6

Equation of line parallel to x – 4y = 0 is y = ¼ x + c

This line cuts rectangle at p ( 0, c) and Q ( 2, c+1/2)

Area of trapezium = ½ x (sum of parallel lines) x ( distance b/w parallel lines)

 $\begin{array}{l}\Rightarrow \frac{1}{2}\times \left(c+c+\frac{1}{2}\right)\times 2=3\\ \Rightarrow 2c+\frac{1}{2}=3\\ \Rightarrow 2c=3-\frac{1}{2}\\ \Rightarrow c=\frac{5}{2}\\ \therefore Theliney=\frac{1}{4}x+\frac{5}{4}\\ \Rightarrow x-4y+5=0\end{array}$