(x-2)^2+(y+1)^2=9 Graph

3 min read Jun 17, 2024

Graphing the Equation (x-2)^2 + (y+1)^2 = 9

The equation (x-2)^2 + (y+1)^2 = 9 represents a circle in the Cartesian coordinate system. Let's break down how to graph it:

Understanding the Equation

This equation is in the standard form of the circle equation:

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

Where:

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

Identifying the Center and Radius

By comparing our equation (x-2)^2 + (y+1)^2 = 9 to the standard form, we can identify:

Center (h, k): (2, -1)
Radius r: √9 = 3

Graphing the Circle

Plot the center: Mark the point (2, -1) on your coordinate plane.
Draw the circle: Using the center as the starting point, measure out a distance of 3 units (the radius) in all directions (up, down, left, right). Mark these points.
Connect the points: Connect the marked points to form a smooth circle.

Key Features of the Graph

Center: The center of the circle is at point (2, -1).
Radius: The radius of the circle is 3 units.
Symmetry: The circle is symmetrical around both the x-axis and y-axis.
Shape: It's a perfect circle, with all points equidistant from the center.

Visualizing the Equation

The equation (x-2)^2 + (y+1)^2 = 9 describes all the points (x, y) that are exactly 3 units away from the point (2, -1). This is why the graph is a circle.