Since, one of the lines represented by ax2+2hxy+ky2=0‌quad bisect the angle between the axes therefore its equation is y=x. Since, y=x satisfies ax2+2hxy+by2=0, therefore ax2+2hx2+bx2=0 ⇒ (a+b)2=4h2 .......(i) Now for equation 4x2+6xy+ky2=0 Here, a=4,h=3,b=k Now from Eq. (i) ⇒ (4+k)2=4(3)2=36 ⇒ 4+k=±6 ⇒ k=2,−10 Hence, k∈{−10,2}