(x-3)^2+(y-4)^2=25

2 min read Jun 17, 2024

Understanding the Equation: (x-3)^2 + (y-4)^2 = 25

This equation represents a circle in the Cartesian coordinate system. Let's break down how to understand its properties:

The Standard Form of a Circle's Equation

The general equation for a circle 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.

Identifying the Center and Radius

In our given equation, (x - 3)^2 + (y - 4)^2 = 25, we can directly identify the center and radius:

Center: (h, k) = (3, 4)
Radius: r^2 = 25, so r = 5

Therefore, this equation describes a circle with a center at (3, 4) and a radius of 5 units.

Visualizing the Circle

To visualize this circle, you can:

Plot the center: Mark the point (3, 4) on a coordinate plane.
Draw the circle: Using the radius of 5 units, draw a circle around the center point.

Key Takeaways

The equation (x-3)^2 + (y-4)^2 = 25 describes a circle.
The center of the circle is located at (3, 4).
The radius of the circle is 5 units.

By understanding the standard form of the circle equation and its components, you can readily identify the center and radius of any circle represented by such an equation.