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(x-3)^2+(y-2)^2=16

2 min read Jun 17, 2024
(x-3)^2+(y-2)^2=16

Understanding the Equation (x-3)^2 + (y-2)^2 = 16

The equation (x-3)^2 + (y-2)^2 = 16 represents a circle in the coordinate plane. Let's break down why:

The Standard Form of a Circle

The general equation for a circle in standard form is:

(x - h)^2 + (y - k)^2 = r^2

Where:

  • (h, k) represents the center of the circle.
  • r represents the radius of the circle.

Applying the Equation

In our equation, (x - 3)^2 + (y - 2)^2 = 16, we can see:

  • (h, k) = (3, 2) This means the center of the circle is at the point (3, 2).
  • r^2 = 16, therefore r = 4. The radius of the circle is 4 units.

Visualizing the Circle

To graph this circle, we would:

  1. Plot the center at (3, 2).
  2. Measure 4 units in every direction (up, down, left, right) from the center.
  3. Connect these points to form a smooth circle.

Key Takeaways

  • The equation (x-3)^2 + (y-2)^2 = 16 defines a circle with a center at (3, 2) and a radius of 4.
  • The standard form of a circle equation allows us to easily identify the center and radius, making it simpler to visualize and graph the circle.

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