The locus of the centre of the circle touching the $X$-axis and passing through the point $(-1,1)$ is

The centres of all circles passing through the points of intersection of the circles $x^2+y^2+2 x-2 y+1=0$ and $x^2+y^2-2 x+2 y-2=0$ and having radius $\sqrt{14}$ lie on the curve

$A$ circle $S$ given by $x^2+y^2-14 x+6 y+33=0$ cuts the $X$-axis at $A$ and $B(O B>O A)$. $C$ is mid-point of $A B . L$ is a line through $C$ and having slope ( -1 ). If $L$ is the diameter of a circle $S^{\prime}$ and also the radical axis of the circles $S$ and $S^{\prime}$, then the equation of the circle $S^{\prime}$ is

For the parabola $y=x^2-3 x+2$, match the items in List I to that of the items in List II. $S$ is a focus, $Z$ is intersection of axis and directrix, $P$ is one end of latus rectum, $Q$ is the point on the parabola at which tangent is parallel to $X$-axis.

$$ \begin{array}{llll} \hline & \text { List I } & & \text { List II } \\ \hline \text { A. } & P & \text { I. } & (2,0) \\ \hline \text { B. } & Q & \text { II. } & \left(\frac{3}{2},-\frac{1}{4}\right) \\ \hline \text { C. } & S & \text { III. } & \left(\frac{3}{2}, 0\right) \\ \hline \text { D. } & Z & \text { IV. } & \left(\frac{3}{2},-\frac{1}{2}\right) \\ \hline & & \text { V. } & \left(0, \frac{3}{2}\right) \\ \hline \end{array} $$