Answer the following by appropriately matching the lists based on the information given in the paragraph
Let the circles $C_1: x^2+y^2=9$ and $C_2:(x-3)^2+(y-4)^2=16$, intersect at the points $X$ and $Y$. Suppose that another circle $\mathrm{C}_3:(\mathrm{x}-\mathrm{h})^2+(\mathrm{y}-\mathrm{k})^2=\mathrm{r}^2$ satisfies the following conditions :
(i) centre of $\mathrm{C}_3$ is collinear with the centres of $\mathrm{C}_1$ and $\mathrm{C}_2$
(ii) $\mathrm{C}_1$ and $\mathrm{C}_2$ both lie inside $\mathrm{C}_3$, and
(iii) $\mathrm{C}_3$ touches $\mathrm{C}_1$ at M and $\mathrm{C}_2$ at N .
Let the line through X and Y intersect $\mathrm{C}_3$ at Z and W , and let a common tangent of $\mathrm{C}_1$ and $\mathrm{C}_3$ be a tangent to the parabola $x^2=8 \alpha y$.
There are some expression given in the List-I whose values are given in List-II below:
Which of the following is the only INCORRECT combination ?
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