(x-6)^2+(y-3)^2=25

2 min read Jun 17, 2024

Understanding the Equation: (x-6)^2 + (y-3)^2 = 25

The equation (x-6)^2 + (y-3)^2 = 25 represents a circle in the Cartesian coordinate system. Let's break down why this is the case and how to interpret the equation.

The Standard Form of a Circle Equation

The general standard form for the equation of 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

Analyzing our Equation

Comparing our equation (x-6)^2 + (y-3)^2 = 25 to the standard form, we can identify the following:

Center: (h, k) = (6, 3)
Radius: r^2 = 25, so r = 5

Graphing the Circle

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

Plot the center: Mark the point (6, 3) on the coordinate plane.
Draw the circle: With the center as the starting point, use the radius (5 units) to draw a circle that passes through points 5 units away in all directions.

Key Takeaways

The equation (x-6)^2 + (y-3)^2 = 25 describes a circle with a center at (6, 3) and a radius of 5.
Understanding the standard form of a circle equation allows us to quickly identify the center and radius, making graphing and analyzing the circle simpler.
This equation represents an infinite set of points that are all equidistant (5 units) from the center point.