(x-6)^2+(y-4)^2-64=0

2 min read Jun 17, 2024

Understanding the Equation: (x-6)^2 + (y-4)^2 - 64 = 0

The equation (x-6)^2 + (y-4)^2 - 64 = 0 represents a circle in the coordinate plane. Here's how we can understand and analyze it:

Standard Form of a Circle

The general standard form 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 the Given Equation

Let's rewrite our given equation to match the standard form:

(x - 6)^2 + (y - 4)^2 = 64

Now we can clearly see that:

Center: (h, k) = (6, 4)
Radius: r^2 = 64 => r = 8

Interpretation

This equation describes a circle with:

Center: at the point (6, 4)
Radius: of 8 units.

Visualizing the Circle

To visualize this circle, you can plot the center point (6, 4) on a coordinate plane. Then, draw a circle with a radius of 8 units around that center point.

Key Points

Understanding the standard form of a circle equation helps in quickly identifying the center and radius of a circle.
The given equation represents a circle with a specific center and radius, allowing for easy visualization and analysis.