Match the conics in Column I with the statements/expressions in Column II :

	Column I		Column II
(A)	Circle	(P)	The locus of the point ($$h,k$$) for which the line $$hx+ky=1$$ touches the circle $$x^2+y^2=4$$.
(B)	Parabola	(Q)	Points z in the complex plane satisfying $$|z+2|-|z-2|=\pm3$$.
(C)	Ellipse	(R)	Points of the conic have parametric representation $$x = \sqrt 3 \left( {{{1 - {t^2}} \over {1 + {t^2}}}} \right),y = {{2t} \over {1 + {t^2}}}$$
(D)	Hyperbola	(S)	The eccentricity of the conic lies in the interval $$1 \le x \le \infty $$.
		(T)	Points z in the complex plane satisfying $${\mathop{\rm Re}\nolimits} {(z + 1)^2} = |z{|^2} + 1$$.

In a triangle $$ABC$$ with fixed base $$BC$$, the vertex $$A$$ moves such that $$$\cos \,B + \cos \,C = 4{\sin ^2}{A \over 2}.$$$

If $$a, b$$ and $$c$$ denote the lengths of the sides of the triangle opposite to the angles $$A, B$$ and $$C$$, respectively, then

The line passing through the extremity $$A$$ of the major axis and extremity $$B$$ of the minor axis of the ellipse $${x^2} + 9{y^2} = 9$$ meets its auxiliary circle at the point $$M$$. Then the area of the triangle with vertices at $$A$$, $$M$$ and the origin $$O$$ is

Tangents drawn from the point P (1, 8) to the circle
$${x^2}\, + \,{y^2}\, - \,6x\, - 4y\, - 11 = 0$$
touch the circle at the points A and B. The equation of the cirumcircle of the triangle PAB is