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. \( r=1 ; \quad(h, k)=(8,6) \) The standard form of the equation of this circle is \( (x-8)^{2}+(y-6)^{2}=1 \). (Type your answer in standard form.) The general form of the equation of this circle is (Simplify your answer. Type an equation.)

The standard form of the circle is:   (x – 8)² + (y – 6)² = 1 To write the equation in general (expanded) form, expand the squares:   (x – 8)² = x² – 16x + 64   (y – 6)² = y² – 12y + 36 Adding these gives:   x² – 16x + 64 + y² – 12y + 36 = 1 Combine like terms:   x² + y² – 16x – 12y + 100 = 1 Subtract 1 from both sides:   x² + y² – 16x – 12y + 99 = 0 Thus, the general form of the equation is:   x² + y² – 16x – 12y + 99 = 0 Graphing: • The center of the circle is at (8, 6). • The radius is 1. This means the circle is a small circle centered at (8,6) with all points exactly 1 unit away from the center. To sketch: 1. Plot the center at (8, 6). 2. Mark points 1 unit away in the horizontal and vertical directions: (9,6), (7,6), (8,7), and (8,5). 3. Draw a smooth curve through these points to complete the circle.