2%2B(y-2)2%3D9-center-and-radius.jpeg "(x+1)2+(y-2)2=9 Center And Radius")
Understanding the Equation: (x + 1)² + (y - 2)² = 9
This equation represents a circle in the standard form of the circle equation:
(x - h)² + (y - k)² = r²
Where:
- (h, k) is the center of the circle
- r is the radius of the circle
Let's break down our equation:
- (x + 1)²: This indicates that the x-coordinate of the center is -1 (since it's written as x + 1, the value of h is -1).
- (y - 2)²: This indicates that the y-coordinate of the center is 2 (since it's written as y - 2, the value of k is 2).
- 9: This represents the square of the radius, so the radius is the square root of 9, which is 3.
Therefore:
- Center of the circle: (-1, 2)
- Radius of the circle: 3
This information allows us to visualize and plot the circle on a coordinate plane. The center of the circle would be located at the point (-1, 2), and all points on the circle would be exactly 3 units away from this center point.