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)(a prime x+b prime y+c prime)=0. The equation of the angle bisectors of the lines represented by the equation 2 x2+x y-3 y2=0 is

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)(a prime x+b prime y+c prime)=0. The equation of the angle bisectors of the lines represented by the equation 2 x2+x y-3 y2=0 is (A) 3 x2+5 x y+2 y2=0 (B) x2-y2-10 x y=0 (C) 3 x2+x y-2 y2=0 (D) x2-y2+10 x y=0

Tardigrade Admin · Accepted Answer

Equation of the pair of angle bisector for the homogenous equation

a x^{2} + 2 h x y + b y^{2} = 0

is given as

\frac{x ^{2} - y ^{2}}{a - b} = \frac{x y}{h}

Here

a = 2, h = 1/2& b = - 3

Equation will become

\frac{x ^{2} - y ^{2}}{2 - ( - 3 )} = \frac{x y}{1/2}

x^{2} - y^{2} = 10 x y

x^{2} - y^{2} - 10 x y = 0

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

$3 x^{2} + 5 x y + 2 y^{2} = 0$

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

$3 x^{2} + x y - 2 y^{2} = 0$

$x^{2} - y^{2} + 10 x y = 0$

Q. The combined equation of the two lines ax+by+c=0 and a′x+b′y+c′=0 can be written as (ax+by+c)(a′x+b′y+c′)=0. The equation of the angle bisectors of the lines represented by the equation 2x2+xy−3y2=0 is

3x2+5xy+2y2=0

x2−y2−10xy=0

3x2+xy−2y2=0

x2−y2+10xy=0

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

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

$3 x^{2} + 5 x y + 2 y^{2} = 0$

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

$3 x^{2} + x y - 2 y^{2} = 0$

$x^{2} - y^{2} + 10 x y = 0$