(x-2)^2+(y+3)^2=25

Jasonbradley

2 min read Jun 17, 2024

Exploring the Circle: (x-2)^2 + (y+3)^2 = 25

The equation (x-2)^2 + (y+3)^2 = 25 represents a circle. Let's break down why and explore its key features:

Understanding the Standard Form

The equation is in the standard form of a circle:

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

where:

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

Identifying the Center and Radius

Comparing our equation (x-2)^2 + (y+3)^2 = 25 to the standard form, we can see:

h = 2
k = -3
r^2 = 25, therefore r = 5

This means:

The center of the circle is at (2, -3)
The radius of the circle is 5 units

Visualizing the Circle

Now that we know the center and radius, we can easily visualize the circle:

Plot the center (2, -3) on a coordinate plane.
From the center, move 5 units up, down, left, and right. These points mark the circle's edge.
Connect these points with a smooth curve to form the circle.

Conclusion

The equation (x-2)^2 + (y+3)^2 = 25 describes a circle centered at (2, -3) with a radius of 5 units. Understanding the standard form allows us to quickly determine a circle's key features and visualize it on a coordinate plane.