2-%2B-y2-%3D-81.jpeg "(x – 5)2 + Y2 = 81")
Exploring the Equation: (x - 5)² + y² = 81
The equation (x - 5)² + y² = 81 represents a circle in the Cartesian coordinate system. Let's break down the components and understand what it signifies:
Understanding the Equation
- (x - 5)²: This term represents the square of the difference between the x-coordinate of a point on the circle and the value 5.
- y²: This term represents the square of the y-coordinate of a point on the circle.
- 81: This value represents the square of the radius of the circle.
Identifying the Circle's Characteristics
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Center: The equation is in the standard form of a circle: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. In our case, the center is (5, 0) because (x - 5) is in the equation, indicating a shift of 5 units to the right on the x-axis.
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Radius: The radius of the circle is the square root of 81, which is 9.
Visualizing the Circle
To visualize the circle, we can plot its center at (5, 0) and draw a circle with a radius of 9 units around it.
Key Points
- The equation (x - 5)² + y² = 81 describes a circle with a center at (5, 0) and a radius of 9 units.
- This equation represents all the points (x, y) that are exactly 9 units away from the point (5, 0).
- By understanding the standard form of a circle, we can quickly identify the center and radius from the equation.