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(x+7)2+(y+8)2=64

2 min read Jun 17, 2024
(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.

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