(x-7)^2+(y+5)^2=4

Jasonbradley

3 min read

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Jun 17, 2024

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Understanding the Equation: (x-7)^2 + (y+5)^2 = 4

The equation (x-7)^2 + (y+5)^2 = 4 represents a circle in the Cartesian coordinate plane. Let's break down the equation to understand its components and what it tells us about the circle.

Key Concepts:

• Standard Form of a Circle: The standard form of the 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 Equation:

• Center: In our equation, (x-7)^2 + (y+5)^2 = 4, we can identify that h = 7 and k = -5. Therefore, the center of the circle is at the point (7, -5).

• Radius: The equation is set equal to 4, which represents r^2. Taking the square root of both sides, we find that r = 2. This means the circle has a radius of 2 units.

Visualizing the Circle:

To graph the circle, follow these steps:

1. Plot the center: Locate the point (7, -5) on the coordinate plane.

2. Draw the radius: From the center, measure out 2 units in all directions (up, down, left, right). These points represent the edge of the circle.

3. Sketch the circle: Connect the points on the edge of the circle to form a smooth curve.

Conclusion:

The equation (x-7)^2 + (y+5)^2 = 4 defines a circle with a center at (7, -5) and a radius of 2 units. By understanding the standard form of a circle's equation, we can easily extract information about its center and radius, allowing us to visualize and graph the circle.