2%2B(y-2)2%3D16-the-center-of-the-circle-is.jpeg "(x-3)2+(y-2)2=16 The Center Of The Circle Is")
Understanding the Equation of a Circle: (x-3)² + (y-2)² = 16
The equation (x-3)² + (y-2)² = 16 represents a circle in the standard form of the circle equation:
(x - h)² + (y - k)² = r²
Where:
- (h, k) represents the center of the circle.
- r represents the radius of the circle.
Finding the Center of the Circle
By comparing the given equation to the standard form, we can easily identify the center:
- h = 3
- k = 2
Therefore, the center of the circle represented by the equation (x-3)² + (y-2)² = 16 is (3, 2).
Visualizing the Circle
To visualize the circle, imagine a point at (3, 2) on a coordinate plane. This point represents the center of the circle. The radius of the circle is the square root of 16, which is 4.
You can then draw a circle with a radius of 4 units around the center point (3, 2).
This visual representation helps understand how the equation defines the circle's position and size on the coordinate plane.