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.)

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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.
The standard form of the circle is $$ (x - 8)^2 + (y - 6)^2 = 1 $$. The general form is $$ x^2 + y^2 - 16x - 12y + 99 = 0 $$. The circle has a center at (8, 6) and a radius of 1.

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