To explain: How to convert the general form of the equation of a circle to the standard form of the equation of a circle.

Expert Solution & Answer

Explanation of Solution

Given information: The general form of the equation of a circle

Calculation:

First step, group the terms and factor out the leading coefficient.

Given:

Ax2+By2+Cx+Dy+E=0 is a circle if A=B .

Divide both sides by the leading coefficient.

Remember, A=B

A(x2+CAx−−)+B(y2+DBy−−)=−E

Now add (12(middle term))2 from each to both sides.

(x2+CAx−−)+(y2+DBy−−)=−EA

Now factor each, what is on right side =r2

(x2+CAx+C24A2)+(y2+DBy+D24B2)=−EA+C24A2+D24B2

C2A=−h and D2A=−k

(x+C2A)2+(y+D2A)2=r2(x−h)2+(y−k)2=r2

Chapter 10.1, Problem 44E

Chapter 10.2, Problem 2CFU

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFU Ch. 10.1 - Prob. 2CFU Ch. 10.1 - Prob. 3CFU Ch. 10.1 - Prob. 4CFU Ch. 10.1 - Prob. 5CFU Ch. 10.1 - Prob. 6CFU Ch. 10.1 - Prob. 7CFU Ch. 10.1 - Prob. 8CFU Ch. 10.1 - Prob. 9CFU Ch. 10.1 - Prob. 10CFU

Ch. 10.1 - Prob. 11CFU Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.2 - Prob. 1CFU Ch. 10.2 - Prob. 2CFU Ch. 10.2 - Prob. 3CFU Ch. 10.2 - Prob. 4CFU Ch. 10.2 - Prob. 5CFU Ch. 10.2 - Prob. 6CFU Ch. 10.2 - Prob. 7CFU Ch. 10.2 - Prob. 8CFU Ch. 10.2 - Prob. 9CFU Ch. 10.2 - Prob. 10CFU Ch. 10.2 - Prob. 11CFU Ch. 10.2 - Prob. 12CFU Ch. 10.2 - Prob. 13CFU Ch. 10.2 - 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