2%2B(y%2B5)2%3D81.jpeg "(x+15)2+(y+5)2=81")
Understanding the Equation: (x + 15)² + (y + 5)² = 81
The equation (x + 15)² + (y + 5)² = 81 represents a circle in the Cartesian coordinate system. To understand this, let's break down the components:
The Standard Form of a Circle
The general equation of a circle in standard form is:
(x - h)² + (y - k)² = r²
Where:
- (h, k) represents the center of the circle.
- r represents the radius of the circle.
Applying the Standard Form
Comparing our equation (x + 15)² + (y + 5)² = 81 to the standard form, we can identify the following:
- Center: Since the equation has (x + 15) and (y + 5), the center of the circle is (-15, -5).
- Radius: The right side of the equation is 81, which is the square of the radius. Therefore, the radius of the circle is √81 = 9.
Visualizing the Circle
Knowing the center and radius, we can easily visualize the circle on a coordinate plane. The circle will be centered at (-15, -5) and have a radius of 9 units.
Key Takeaways
- The equation (x + 15)² + (y + 5)² = 81 represents a circle centered at (-15, -5) with a radius of 9.
- By understanding the standard form of a circle equation, we can quickly identify the center and radius of any given circle.
This equation is a powerful tool to understand and visualize circles, which are fundamental geometric shapes with numerous applications in various fields.