Write the standard form of the equation and the general form of the equation of the circle with radius \( r \) and center \( (h, k) \). Then graph the circle. \( r=1 ; \quad(h, k)=(0,-1) \) The standard form of the equation of this circle is

For a circle with radius r and center (h, k): • The standard form equation is: (x - h)² + (y - k)² = r² • The general form equation is: x² + y² - 2hx - 2ky + (h² + k² - r²) = 0 Given r = 1 and (h, k) = (0, –1): 1. Substitute into the standard form:   (x - 0)² + (y - (–1))² = 1²   x² + (y + 1)² = 1 2. To derive the general form, expand the standard form:   x² + (y + 1)² = x² + (y² + 2y + 1) = 1   x² + y² + 2y + 1 = 1   x² + y² + 2y = 0 Thus, the answers are: • Standard form: x² + (y + 1)² = 1 • General form: x² + y² + 2y = 0 Graphing the circle: 1. Plot the center at (0, –1). 2. Since r = 1, from the center you can measure one unit in all directions.   – To the right: (1, –1)   – To the left: (–1, –1)   – Upward: (0, 0)   – Downward: (0, –2) 3. Draw a circle that passes through these four points, ensuring an even distance around the center. This completes the solution.