Question

If the adjacent sides of a parallelogram are represented by $2x^2-5xy+3y^2=0$ and the equation of one diagonal is $x+y-2=0,$ then the equation of the other diagonal is

• A. $9x-11y=0$
• B. $9x+11y=0$
• C. $11x-9y=0$
• D. $11x+9y=0$

Answer 1

The correct option is A $9x-11y=0$

$2x^2-5xy+3y^2=0$
$\Rightarrow 2x^2-2xy-3xy+3y^2=0$
$\Rightarrow (x-y)(2x-3y)=0$
So, equation of the adjacent sides are $y=x,y=\frac{2x}{3}$


Given diagonal equation does not pass through the origin.
So, equation of $AC$ is $x+y-2=0$
$OA\equiv y=x$ and $OC\equiv y=\frac{2x}{3}$
$\Rightarrow A\equiv (1,1)$ and $C\equiv (\frac{6}{5},\frac{4}{5})$
So, coordinates of $B\equiv (\frac{11}{5},\frac{9}{5})$
Equation of $OB$ is $y=\frac{9/5}{11/5}x$
$\Rightarrow 11y=9x$
$\Rightarrow 9x-11y=0$