Question

Find the center and the length of a radius of each circle. $x^{2}+y^{2}-2 x-6 y-6=0$

Name: Problem 23, Chapter 8: Intermediate Algebra
Uploaded: 2022-03-18T00:21:52-08:00
Duration: 48 s
Channel: James Kiss
Description: Find the center and the length of a radius of each circle. x^2+y^2-2 x-6 y-6=0

   Find the center and the length of a radius of each circle.
 $x^{2}+y^{2}-2 x-6 y-6=0$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 8, Problem 23

Instant Answer

Solved by Expert James Kiss

03/18/2022

Step 1

We can rewrite this equation by grouping the x terms and y terms together. This gives us $(x^{2}-2x)+(y^{2}-6y)=-6$. Show more…

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Find the center and the length of a radius of each circle. $x^{2}+y^{2}-2 x-6 y-6=0$

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Key Concepts

Completing_the_Square

Completing the square is a method used to rewrite quadratic equations in a form that reveals key properties of geometric figures, such as circles. By grouping and rearranging terms, you can form perfect square trinomials, which is essential for deriving the standard form of a circle's equation.

Standard_Form_of_a_Circle

The standard form of a circle's equation is (x - h)² + (y - k)² = r². This form directly shows the circle's center at (h, k) and its radius r. Converting a general circle equation into this form helps in easily identifying these attributes and understanding the circle's geometry.

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