뒤로Equations of Circles: Finding Center and Radius
스터디 가이드 - 스마트 노트
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Equations of Circles
Standard Form of a Circle
The equation of a circle in the coordinate plane is commonly written in standard form as:
Standard Form:
(h, k) is the center of the circle.
r is the radius of the circle.
Identifying Center and Radius
Given the equation:
Center: Compare with the standard form. The term means . The term can be rewritten as , so .
Radius: The right side of the equation is , so .
Summary Table
Feature | Value |
|---|---|
Center | (6, -7) |
Radius | 7 |
Example
Example: For the equation , the center is (2, -5) and the radius is .
Applications
Finding the center and radius is useful for graphing circles and solving geometric problems in algebra.
Circle equations appear in analytic geometry, physics, and engineering contexts.
