AP EAMCET Engineering 2011 Solved Paper

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}