standard_description: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
problem_activity: Task
This problem examines equations defining different circles in the $x$-$y$ plane.
Use the Pythagorean theorem to
find an equation in $x$ and $y$ whose solutions are the points on the circle  of radius 2 with center $(1,1)$  and explain why it works.
Suppose $r$ is a positive number and $(a,b)$ a point in the plane.
Use the Pythagorean theorem to
find an equation in $x$ and $y$ whose solutions are the points on the circle of radius $r$ with center $(a,b)$ and explain why it works.


aligns: no