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Find the center and the radius of the circle represented by each equation. a. $x^{2}+y^{2}-8 y=9$ b. $(x+7)^{2}+y^{2}+6 y=27$ $c. x^{2}+10 x+y^{2}-12 y=-10$ d. $x^{2}+y^{2}=8 x-14 y+35$

Name: Problem 11, Chapter 13: Geometry for Enjoyment and Challenge
Uploaded: 2021-08-17T18:29:44-08:00
Duration: 6 min 58 s
Channel: Debasish Das
Description: Find the center and the radius of the circle represented by each equation. a. x^2+y^2-8 y=9 b. (x+7)^2+y^2+6 y=27 c. x^2+10 x+y^2-12 y=-10 d. x^2+y^2=8 x-14 y+35

   Find the center and the radius of the circle represented by each equation.
a. $x^{2}+y^{2}-8 y=9$
b. $(x+7)^{2}+y^{2}+6 y=27$
$c.  x^{2}+10 x+y^{2}-12 y=-10$
d. $x^{2}+y^{2}=8 x-14 y+35$

Geometry for Enjoyment and Challenge

Richard Rhoad,… 1st Edition

Chapter 13, Problem 11

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Solved by Expert Debasish Das

08/17/2021

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We need to rewrite the given equations in this form to find the center and the radius. a) $x^{2}+y^{2}-8 y=9$ Show more…

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Find the center and the radius of the circle represented by each equation. a. $x^{2}+y^{2}-8 y=9$ b. $(x+7)^{2}+y^{2}+6 y=27$ $c. x^{2}+10 x+y^{2}-12 y=-10$ d. $x^{2}+y^{2}=8 x-14 y+35$

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Key Concepts

Standard Form of a Circle

The standard form for the equation of a circle is written as (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r is its radius. Converting a circle's equation into this form allows one to easily identify these key characteristics.

Completing the Square

Completing the square is a technique used to rewrite quadratic expressions as a perfect square trinomial. In the context of circles, this method is applied separately to the x and y terms in a general quadratic equation so that it can be transformed into the standard form, thus revealing the circle's center and radius.

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