The combined equation of the angle bisectors of the lines represented by 2x2+xy−y2−10x+2y+8=0 is

a=2,2h=1,b=−1,2g=−10,2f=2,c=8Point of intersection is (x1,y1)=hf−bgab−h2,gh−afab−h2=(2,2)The pair of angular bisectors is h(x−x1)2−(y−y1)2=(a−b)(x−x1)(y−y1)⇒12(x−2)2−(y−2)2=(2+1)(x−2)(y−2)⇒x2−y2−4x+4y=6(xy−2x−2y+4)⇒x2−6xy−y2+8x+16y−24=0