Question

The combined equation of the two lines $a x+b y+c=0$ and $a^{\prime} x+b^{\prime} y+c^{\prime}=0$ can be written as $(a x+b y+c)\left(a^{\prime} x+b^{\prime} y+c^{\prime}\right)=0$
The equation of the angle bisectors of the lines represented by the equation $2 x^2+x y-3 y^2=0$ is

• A. $3 x^2+5 x y+2 y^2=0$
• B. $x^2-y^2-10 x y=0$
• C. $3 x^2+x y-2 y^2=0$
• D. $x^2-y^2+10 x y=0$

Answer 1

Answer: (B)

$x^2-y^2-10 x y=0$

Answer 2

Equation of the pair of angle bisector for the homogenous equation ax2+2hxy+by2=0 is given as
a−bx2−y2​=hxy​
Here a=2,h=1/2&b=−3
Equation will become
2−(−3)x2−y2​=1/2xy​
x2−y2=10xy
x2−y2−10xy=0