# Problem 8. II variant.

On the coordinate plane $O a b$, plot the set of points for which the system $\left\{\begin{array}{l}x^{2}+y^{2}=a^{2}, \\ x+|y|=b\end{array}\right.$

has at least one solution.
Solution. The graph of the first equation is a circle of radius $|a|$ centered at the origin; the graph of the second equation is a "corner" with its vertex at coordinates $(b; 0)$ (see figure). The system has a solution if the condition $-|a| \leq b \leq \sqrt{2}|a|$ is satisfied.

The set of points in the plane $O a b$ that satisfy this condition is shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_1cdabbf1f496496d2444g-07.jpg?height=617&width=660&top_left_y=1556&top_left_x=1269)

N

Grading criteria for 9th grade assignments

| Assignment | $\mathbf{1}$ | $\mathbf{2}$ | $\mathbf{3}$ | $\mathbf{4}$ | $\mathbf{5}$ | $\mathbf{6}$ | $\mathbf{7}$ | $\mathbf{8}$ | Total |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| Points | 8 | 10 | 10 | 12 | 12 | 16 | 16 | 16 | $\mathbf{1 0 0}$ |