Final answer:
The general form of the circle with center (2,-3) and radius 2 is x² - 4x + y² + 6y + 5 = 0.
Step-by-step explanation:
To express the given center-radius form of the circle with center C (2,-3) and radius r=2 in the general form, we use the standard equation of a circle.
The general form of a circle is:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius. Substituting the given values, we have:
(x - 2)² + (y + 3)² = 2²
Expanding the squares and simplifying, we get:
(x² - 4x + 4) + (y² + 6y + 9) = 4
Rearranging everything to one side:
x² - 4x + y² + 6y + 9 = 0
The general form of the circle is therefore:
x² - 4x + y² + 6y + 5 = 0