JEE Advanced · 2019 · 27 May 2019 · Paper 2 · Circle

Answer the following by appropriately matching the lists based on the information given in the paragraph
Let the circles ${\mathrm{C}}_1:{\mathrm{x}}^2+{\mathrm{y}}^2=9$ and ${\mathrm{C}}_2:(\mathrm{x}-3{)}^2+(\mathrm{y}-4{)}^2=16$, 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 ${\mathrm{x}}^2=8\alpha \mathrm{y}$.

There are some expression given in the List-I whose values are given in List-II below:

Which of the following is the only CORRECT combination ?