Equation  $3x^4-8x^{3}y-8x{y}^3-3y^4-3x^2+8xy+3y^2=0$ can be written as $S.P=0$ where  $S=0$  represent circle and  $P=0$ represent pair of lines. Let A , B, C, D be the points of intersection of  $P=0andS=0$. If tangents at A , B , C , D on circle $S=0$  intersect at K,L,M,N then area of circumcircle of KLMN is k $\pi$, then k is equal to ___