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(x-2)^2+(y+3)^2=9 Graph

2 min read Jun 17, 2024
(x-2)^2+(y+3)^2=9 Graph

Understanding the Graph of (x - 2)^2 + (y + 3)^2 = 9

The equation (x - 2)^2 + (y + 3)^2 = 9 represents a circle. To understand how to graph it, let's break down the equation and its components.

Standard Form of a Circle

The standard form of a circle's equation is:

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

Where:

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

Analyzing the Equation

Comparing our equation (x - 2)^2 + (y + 3)^2 = 9 to the standard form, we can identify the following:

  • Center: (h, k) = (2, -3)
  • Radius: r^2 = 9, so r = 3

Graphing the Circle

  1. Locate the center: Plot the point (2, -3) on the coordinate plane.
  2. Draw the radius: From the center, move 3 units in all directions (up, down, left, right). This will give you four points on the circle's circumference.
  3. Connect the points: Draw a smooth curve connecting the four points, forming the complete circle.

Key Points

  • The equation defines all points on the circle that are 3 units away from the center (2, -3).
  • The square root of the constant term on the right side of the equation gives you the radius.
  • The values within the parentheses (h, k) represent the opposite signs of the coordinates of the center.

By understanding the standard form of a circle equation and identifying the center and radius, you can easily graph any circle equation.

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