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

3 min read Jun 17, 2024

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

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

Understanding the Standard Form

The equation is in the standard form of a circle's 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

Analyzing the Equation

In our case:

(h, k) = (3, 0), indicating the center of the circle is at the point (3, 0).
r^2 = 9, so r = 3, indicating the radius of the circle is 3 units.

Key Features

Center: The center of the circle is located at (3, 0).
Radius: The radius of the circle is 3 units.
Symmetry: The circle is symmetrical about both the x-axis and the y-axis.
Domain and Range: The domain of the circle is [0, 6] and the range of the circle is [-3, 3].

Graphing the Circle

To graph the circle, follow these steps:

Locate the center: Plot the point (3, 0) on the coordinate plane.
Draw the radius: From the center, draw a line segment of length 3 units in all four directions (up, down, left, and right).
Connect the points: Connect the endpoints of these radius lines to form a smooth circle.

Conclusion

The equation (x-3)^2 + y^2 = 9 describes a circle with a center at (3, 0) and a radius of 3 units. By understanding the standard form of a circle's equation, we can easily extract key information like the center, radius, and graph the circle accurately.