2%2B(y-6)2%3D81.jpeg "(x-5)2+(y-6)2=81")
Understanding the Equation: (x-5)^2 + (y-6)^2 = 81
This equation represents a circle in the standard form. Let's break down the components and understand its significance:
Standard Form of a Circle:
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.
Applying it to our equation:
In our case, we have: (x - 5)^2 + (y - 6)^2 = 81
Comparing this to the standard form, we can identify:
- Center (h, k): (5, 6)
- Radius (r): √81 = 9
Interpretation:
This equation describes a circle with a center at the point (5, 6) and a radius of 9 units.
Visual Representation:
To visualize this circle, imagine plotting the center point (5, 6) on a coordinate plane. From this point, you would draw a circle with a radius of 9 units extending in all directions.
Key Points to Remember:
- The equation (x-5)^2 + (y-6)^2 = 81 represents a circle.
- The center of the circle is (5, 6).
- The radius of the circle is 9 units.
By understanding the standard form and the components of the equation, we can easily identify the properties of the circle and visualize its shape.