Circle Center and Radius from Equation
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Questions and Answers

A circle can be represented by the equation: (x - ______)^2 + (y - k)^2 = r^2

h

To find the ______ and radius from the equation, follow these steps:

center

Identify the values of h and k from the equation, which represent the ______ (h, k)

center

Identify the value of r from the equation, which represents the ______

<p>radius</p> Signup and view all the answers

The ______ of the circle is the point (h, k) in the equation (x - h)^2 + (y - k)^2 = r^2

<p>center</p> Signup and view all the answers

The ______ of the circle is the value of r in the equation (x - h)^2 + (y - k)^2 = r^2

<p>radius</p> Signup and view all the answers

Study Notes

Circle Center and Radius from Equation

Circle Equation

  • A circle can be represented by the equation: (x - h)^2 + (y - k)^2 = r^2
  • Where (h, k) is the center of the circle and r is the radius

Finding the Center and Radius

  • To find the center and radius from the equation, follow these steps:
  1. Write the equation in the standard form: (x - h)^2 + (y - k)^2 = r^2
  2. Identify the values of h and k from the equation, which represent the center (h, k)
  3. Identify the value of r from the equation, which represents the radius

Examples

  • Equation: (x - 2)^2 + (y - 3)^2 = 16
    • Center: (2, 3)
    • Radius: 4 (since r^2 = 16, r = √16 = 4)
  • Equation: (x + 1)^2 + (y - 2)^2 = 25
    • Center: (-1, 2)
    • Radius: 5 (since r^2 = 25, r = √25 = 5)

Key Concepts

  • The center of the circle is the point (h, k) in the equation (x - h)^2 + (y - k)^2 = r^2
  • The radius of the circle is the value of r in the equation (x - h)^2 + (y - k)^2 = r^2

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Description

Find the center and radius of a circle from its equation in standard form. Learn how to identify the values of h, k, and r from the equation and calculate the radius.

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