%5E2%2B(y-4)%5E2-64%3D0.jpeg "(x-6)^2+(y-4)^2-64=0")
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.