The joint equation of pair of lines passing through (2,3) and parallel to the line =0
The joint equation of pair of lines passing through (2,3) and parallel to the line
=0
$x^{2}-y^{2}-4 x+6 y-5=0$
$x^{2}-y^{2}-4 x+6 y=0$
$x^{2}-y^{2}-4 x+6 y+17=0$
$x^{2}-y^{2}-4 x+6 y+2=0$
Solution
$x^{2}-y^{2}=0 \Rightarrow(x-y)(x+y)=0$
Thus slopes of given lines are 1 and $-1$.
The eq. of lines passing through $(2,3)$ and parallel to given liens are
$(y-3)=(x-2)$ and $(y-3)=-(x-2)$ i.e.
$x-y+1=0$ and $(x+y-5)=0$
Hence required eq. is
$(x-y+1)(x+y-5)=0$
$x^{2}-x y+x+x y-y^{2}+y-5 x+5 y-5=0$
$x^{2}-y^{2}-4 x+6 y-5=0$