Solution:
We know that the formula to write the equation of a circle is (x – h)² + (y – k)² = r², where:
- h = x coordinate
- k = y-coordinate
- r = radius of circle
- Center of circle: (-6,2)
First, let's find the radius of the circle. We know that the diameter of the circle is ten units. The radius is half of the diameter. This means that the radius is five units because it is half the diameter, which is ten units.
- Diameter: 10 units
- Radius: 10/2 units = 5 units
Creating the equation:
- (x – h)² + (y – k)² = r²
- => (x + 6)² + (y – 2)² = 5²
Hence, the equation to form a circle with center (-6, 2) and diameter 10 is (x + 6)² + (y – 2)² = 5².
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