Q. The four sides of a quadrilateral are given by the equation $xy(x - 2)(y - 3) = 0$. The equation of the line parallel to $x - 4y = 0$ that divides the quadrilateral in two equal area is
A) $x - 4y + 5 = 0$
B) $x - 4y - 5 = 0$
C) $4y = x + 1$
D) $4y + 1 = x$
Explanation
(a)
Equation of sides are $x = 0,\ x = 2,\ y = 0,\ y = 3$
[image:10_image8.emf]
$Line\ parallel\ to\ y = \frac{1}{4}\ x\ is\ y = \frac{1}{4}\ x + \lambda$
Clearly, $AC = BF$
$\Rightarrow \ \lambda = 3 - \lambda - \frac{1}{2}\ \Rightarrow \lambda = \frac{5}{4}$
$\therefore\$Equation of required line is $x - 4y + 5 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.