Question

Write the equation of each circle with the given center and radius. Center $(-6,-1)$, radius 15

Name: Problem 74, Chapter 10: Intermediate Algebra for College Students
Uploaded: 2020-04-23T22:13:00-08:00
Duration: 40 s
Channel: Heather Zimmers
Description: Write the equation of each circle with the given center and radius. Center (-6,-1), radius 15

   Write the equation of each circle with the given center and radius.
Center $(-6,-1)$, radius 15

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 10, Problem 74

Instant Answer

Solved by Expert Heather Zimmers

04/23/2020

Step 1

Step 1: Recall the equation of a circle with center (h, k) and radius r: (x - h)^2 + (y - k)^2 = r^2 Show more…

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Write the equation of each circle with the given center and radius. Center $(-6,-1)$, radius 15

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Key Concepts

Center and Radius

Understanding the center and radius is crucial because the center determines the circle's location on the coordinate plane and the radius defines its size. The values of h and k are substituted directly into the standard form, and the radius r is squared to complete the equation.

Standard Form of a Circle

The standard form of a circle’s equation is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r is the radius. This form directly links the geometry of the circle to its algebraic equation by expressing a set of points that are at a constant distance, r, from the center.

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