Question

Find the joint equation of lines passing through $(-2,3)$ and parallel to the bisector of the angles between the co-ordinate axes.

Answer 1

Bisector of coordinate axes are $y=x$ and $y=-x$

Now first line be $y=x+c$

pass through $(-2,3)$

$3=-2+c\Rightarrow c=5$

$L_1:y=x+5$

Now second line be $y=-x+d$

$3+2+d\Rightarrow d=1$

$L_2:y=-x+1$

Joint equation: $(y-x-5)(y+x-1)=0$

$\Rightarrow$ $y^2-x^2-4x-6y+5=0$