(x-2)^2+(y-3)^2=16

Jasonbradley

2 min read Jun 17, 2024

Understanding the Equation: (x-2)^2 + (y-3)^2 = 16

This equation represents a circle in the Cartesian coordinate system. Let's break down why:

The Standard Equation of a Circle

The standard form of a circle's equation 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 - 2)^2 + (y - 3)^2 = 16, to the standard form, we can identify the following:

Center: (h, k) = (2, 3)
Radius: r^2 = 16, therefore r = 4

Visualizing the Circle

Now that we know the center and radius, we can easily visualize the circle. It's centered at the point (2, 3) and has a radius of 4 units. This means that every point on the circle is exactly 4 units away from the point (2, 3).

Key Points to Remember

The equation (x-2)^2 + (y-3)^2 = 16 defines a circle with a specific center and radius.
Understanding the standard form of a circle's equation allows us to quickly identify its center and radius.
This equation is a fundamental concept in geometry and can be used to solve various problems related to circles.