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(x-1)^2+(y+3)^2=4 Graph

3 min read Jun 17, 2024
(x-1)^2+(y+3)^2=4 Graph

Understanding the Graph of (x-1)^2 + (y+3)^2 = 4

The equation (x-1)^2 + (y+3)^2 = 4 represents a circle in the Cartesian coordinate system. Let's break down why and how to graph it.

The Standard Circle Equation

The standard form of a circle's equation 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.

Analyzing our Equation

Comparing our given equation (x-1)^2 + (y+3)^2 = 4 to the standard form, we can identify the following:

  • Center: (h, k) = (1, -3)
  • Radius: r^2 = 4, so r = 2

Graphing the Circle

  1. Plot the Center: Locate the point (1, -3) on the coordinate plane. This will be the center of our circle.

  2. Mark the Radius: From the center, move 2 units to the right, left, up, and down. These points will lie on the circle's circumference.

  3. Connect the Points: Connect the points you marked in step 2 with a smooth curve to form the complete circle.

Key Points

  • The equation (x-1)^2 + (y+3)^2 = 4 defines all the points that are exactly 2 units away from the point (1, -3). This is the very definition of a circle.
  • The radius determines the size of the circle. A larger radius will result in a larger circle.
  • The center determines the circle's position on the coordinate plane.

By understanding the standard circle equation and its components, you can easily graph any circle equation in the form (x - h)^2 + (y - k)^2 = r^2.

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