We can say that both line passes through point $(5, 3)$ and makes angle ${{45}^o \mathrm{a}\mathrm{n}\mathrm{d} 135}^o$ with x-axis
$\therefore$ Equation of first line is,
$y-3=\tan {45}^o(x-5)$
$y-3=x-5$
$y-x+2=0$ .....(i)
Similarly,
$y-3=\tan {135}^o(x-5)$
$y-3=-1(x-5)$
$y+x-8=0$ ...... (ii)
$\therefore$ Joint equation of line is
$\left(y-x+2\right)\left(y+x-8\right)=0$
$\Rightarrow x^2-y^2-10x+6y+16=0$