From the point T(-6,1), two tangents are drawn to the parabola y^2=4x, touching it at A and B.

The tangent at $(t^2,2t)$ is $ty=x+t^2$. It passes through $T$ if $t^2-t-6=0$, so $t=3,-2$ and the contact points are $A(9,6)$, $B(4,-4)$. (A) The chord of contact is $T$-polar: $y\cdot1=2(x-6)$, i.e. $2x-y=12$; it contains both $A$ and $B$; correct. (B) Area $=\tfrac12\left|-6(6+4)+9(-4-1)+4(1-6)\right|=\tfrac{125}{2}$ (also $\tfrac12|t_1-t_2|^3$); correct. (C) The circumcircle of $TAB$ is $x^2+y^2-3x-7y-48=0$, which at $(1,0)$ gives $-50\ne0$; the focus property belongs to the triangle formed by three tangents, not to the triangle with the contact points; incorrect. (D) The slopes are $\tfrac13$ and $-\tfrac12$, product $-\tfrac16\ne-1$ (the angle is $45^\circ$); incorrect. Answer: A and B.