Question

If the lines represented by $a{x}^2+8xy+3y^2=0$ are mutually perpendicular, then

• A. $x-3y=0$ is one of the line representing pair of lines
• B. $|a|=3$
• C. $y-3x=0$ is one of the line representing pair of lines
• D. $|a|=\frac{8}{3}$

Answer 1

Answer: (A), (B)

$|a|=3$

The lines given by $a{x}^2+5xy+3y^2=0$ are mutually perpendicular if
$\text{coefficient of}{x}^2+\text{coefficient of}{y}^2=0$
$\Rightarrow a+3=0$
$\Rightarrow a=-3$
$\therefore |a|=3$
Now $-3x^2+8xy+3y^2=0$
$\Rightarrow -3x^2+9xy-xy+3y^2=0\Rightarrow (3y-x)(y+3x)=0$
So the lines will be
$x=3y;y+3x=0$