### Circles

Package of problems

## Problem

We have thought of 13 circles. 11 of them are drawn accurately on the above graph. Here are the equations of 11 of the original 13 circles.

1. $(x+10)^2 +(y+15)^2 = 4\pi^2$
2. $x^2 + y^2 = 324$
3. $(x+22)^2 + (y+36)^2 = 411$
4. $(x+3\pi)^2 + (y-15)^2 = 1990$
5. $\bigl(x-21\sqrt{2}\bigr)^2 + \bigl(y-24\sqrt{3}\bigr)^2 = 131\sqrt{5}$
6. $x^2 + y^2 + 66x - 78y + 2110 = 0$
7. $x^2 + y^2 = 9$
8. $(x-23)^2 +(y+42)^2 = 200$
9. $x^2 + y^2 = 81$
10. $(x-18)^2 + (y+36)^2 = 1990$
11. $x^2 + y^2 - 18x + 45 = 0$

Can you match them up, find the two missing equations and draw the two missing circles on the graph?