%5E2%2B(y-3)%5E2%3D9-circumference.jpeg "(x+2)^2+(y-3)^2=9 Circumference")
Understanding the Equation and its Circumference
The equation (x + 2)^2 + (y - 3)^2 = 9 represents a circle in the standard form of the circle equation:
(x - h)^2 + (y - k)^2 = r^2
Where:
- (h, k) represents the center of the circle.
- r represents the radius of the circle.
From our given equation, we can identify:
- Center: (-2, 3)
- Radius: √9 = 3
Therefore, the circle represented by the equation has a center at (-2, 3) and a radius of 3.
Calculating the Circumference
The circumference of a circle is the distance around its boundary. It is calculated using the formula:
Circumference (C) = 2πr
Where:
- π (pi) is a mathematical constant approximately equal to 3.14159
- r is the radius of the circle.
Using the radius of our circle (r = 3), we can calculate its circumference:
C = 2π(3) = 6π
Therefore, the circumference of the circle represented by the equation (x + 2)^2 + (y - 3)^2 = 9 is 6π units.