Jasonbradley
Home

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

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

Understanding the Equation: (x - 2)^2 + (y + 3)^2 = 9

The equation (x - 2)^2 + (y + 3)^2 = 9 represents a circle in the coordinate plane. Let's break down why:

The Standard Form of a Circle

The general 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 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

Graphical Representation

This information allows us to easily plot the circle on a graph.

  1. Locate the Center: Start by marking the point (2, -3) on the coordinate plane.
  2. Draw the Radius: From the center, measure out a distance of 3 units in all directions (up, down, left, right).
  3. Sketch the Circle: Connect the points you marked in step 2 to form a smooth circle.

Key Takeaways

  • The equation (x - 2)^2 + (y + 3)^2 = 9 describes a circle centered at (2, -3) with a radius of 3.
  • Understanding the standard form of a circle's equation makes it easy to identify its center and radius.
  • This information enables you to visually represent the circle on a graph.

Related Post

Featured Posts