Question

The for 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. $4y+1=1$

Answer 1

The correct option is A $x-4y+5=0$

Solution -

REF. Image

Let line $y=\frac{x}{4}+c$ divides quadrilateral ABCD

in two equal halves

then ${\int }_0^2(\frac{x}{4}+c)dx=\frac{3\times 2}{2}$

${[\frac{x^2}{8}+cx]}_0^2=3$

$\frac{4}{8}+2c=3$

$2c=\frac{5}{2}$ $c=\frac{5}{4}$

then line is

$y=\frac{x}{4}+\frac{5}{4}$

$x-4y+5=0$

A is correct.