(x-3)2+(y-2)2=16 The Center Of The Circle Is

2 min read Jun 17, 2024
(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.

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