The combined equation of the two lines ax+by+c=0 and a'x+b'y+c'=0 can be written as (ax+by…

Question

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 $2x^2+xy-3y^2=0$ is :

Accepted Answer

For pair of straight lines in this form

$a x^2+b y^2+2 h x y+2 g x+2 f y+c=0$

Equation of angle bisector is

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

for $2 x^2+x y-3 y^2=0$

$$
a=2, b=-3, h=\frac{1}{2}
$$

Equation of angle bisector is

$$
\begin{aligned}
& \frac{x^2-y^2}{5}=\frac{x y}{1 / 2} \\
& \Rightarrow \mathrm{x}^2-\mathrm{y}^2-10 \mathrm{xy}=0
\end{aligned}
$$

Solutions · 1