2%2B(y%2B8)2%3D64.jpeg "(x+7)2+(y+8)2=64")
Exploring the Equation: (x+7)² + (y+8)² = 64
This equation represents a circle in the coordinate plane. Let's break down why:
Understanding the Standard Form of a Circle
The standard form of the equation of a circle is:
(x - h)² + (y - k)² = r²
where:
- (h, k) represents the coordinates of the center of the circle
- r represents the radius of the circle
Analyzing our Equation
Comparing our given equation, (x + 7)² + (y + 8)² = 64, with the standard form, we can identify the following:
- Center: The center of the circle is at (-7, -8). Notice that the signs inside the parentheses are opposite of what we see in the standard form.
- Radius: The radius is 8, since 64 is the square of 8 (64 = 8²).
Visualizing the Circle
Now that we know the center and radius, we can easily visualize the circle. It's centered at (-7, -8) and extends 8 units in all directions.
Key Points
- The given equation defines a circle in the coordinate plane.
- It provides information about the center and radius of the circle.
- Understanding the standard form of the circle equation is crucial for identifying these characteristics.
This knowledge allows us to graph the circle accurately and explore its properties further.