Identify the locus of all points P(x, y) in the plane satisfying each of the following expressions:
a. x^2 + y^2 < R^2
b. x^2 + y^2 - 2x + 2y + 4 = 0
Your textbook or class discussion must say something about a. The answer to b is a circle, a point, or the empty set. You can find the details by completing the square, i.e., representing the equation as $\displaystyle (x-x_0)^2+(y-y_0)^2=c$ for some constants $\displaystyle x_0$, $\displaystyle y_0$ and $\displaystyle c$.