Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Question

Chapter 15.2, Problem 57E

To determine

Write the standard form of circle equation.

Expert Solution & Answer

Answer to Problem 57E

(x+16)2+(y−76)2=16918

Explanation of Solution

Given information:

Given points,

(2,−1),(−3,0), and(1,4)

Calculation:

The standard form of equation of circle passing through (x,y) with centre (f,g) is given by,

x2+y2+2gx+2fy+c=0

When circle passes through points, (2,−1) we get,

22+(−1)2+2g(2)+2f(−1)+c=04g−2f+c=−5.....(1)now passes through points (−3,0)(−3)2+(0)2+2g(−3)+2f(0)+c=06g−c=9.....(2)now passes through points (1,4)(1)2+(4)2+2g(1)+2f(4)+c=02g+8f+c=−17.....(3)

Now solve the equation,

4(4g−2f+c=−5) [multiply by 4 and add]16g−8f+4c=−202g+8f+c=−17_18g+5c=−37now,add5×(6g−c=9) we get30g−5c=4518g+5c=−37_48g=8g=16

Now substitute g=1/6 in 6g−c=9 we get,

6(16)−c=91−c=9c=−8

Now put c=−8,g=1/6 in equation 4g−2f+c=−5 we get,

4(1/6)−2f+(−8)=−5f=−76

(x+16)2+(y−76)2=16918

Hence, the equation of circle passing through given points is, (x+16)2+(y−76)2=16918 .

Chapter 15.2, Problem 56E

Chapter 15.2, Problem 58E

Chapter 15 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 15.1 - Prob. 1GCE Ch. 15.1 - Prob. 2GCE Ch. 15.1 - Prob. 3GCE Ch. 15.1 - Prob. 4GCE Ch. 15.1 - Prob. 5GCE Ch. 15.1 - Prob. 1CFU Ch. 15.1 - Prob. 2CFU Ch. 15.1 - Prob. 3CFU Ch. 15.1 - Prob. 4CFU Ch. 15.1 - Prob. 5CFU

Ch. 15.1 - Prob. 6CFU Ch. 15.1 - Prob. 7CFU Ch. 15.1 - Prob. 8CFU Ch. 15.1 - Prob. 9CFU Ch. 15.1 - Prob. 10CFU Ch. 15.1 - Prob. 11CFU Ch. 15.1 - Prob. 12E Ch. 15.1 - Prob. 13E Ch. 15.1 - Prob. 14E Ch. 15.1 - Prob. 15E Ch. 15.1 - Prob. 16E Ch. 15.1 - Prob. 17E Ch. 15.1 - Prob. 18E Ch. 15.1 - Prob. 19E Ch. 15.1 - Prob. 20E Ch. 15.1 - Prob. 21E Ch. 15.1 - Prob. 22E Ch. 15.1 - Prob. 23E Ch. 15.1 - Prob. 24E Ch. 15.1 - Prob. 25E Ch. 15.1 - Prob. 26E Ch. 15.1 - Prob. 27E Ch. 15.1 - Prob. 28E Ch. 15.1 - Prob. 29E Ch. 15.1 - Prob. 30E Ch. 15.1 - Prob. 31E Ch. 15.1 - Prob. 32E Ch. 15.1 - Prob. 33E Ch. 15.1 - Prob. 34E Ch. 15.1 - Prob. 35E Ch. 15.1 - Prob. 36E Ch. 15.1 - Prob. 37E Ch. 15.1 - Prob. 38E Ch. 15.1 - Prob. 39E Ch. 15.1 - Prob. 40E Ch. 15.1 - Prob. 41E Ch. 15.1 - Prob. 42E Ch. 15.1 - Prob. 43E Ch. 15.1 - Prob. 44E Ch. 15.1 - Prob. 45E Ch. 15.1 - Prob. 46E Ch. 15.1 - Prob. 47E Ch. 15.1 - Prob. 48E Ch. 15.1 - Prob. 49E Ch. 15.1 - Prob. 50E Ch. 15.1 - Prob. 51E Ch. 15.1 - Prob. 52E Ch. 15.1 - 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Prob. 12CFU Ch. 15.4 - Prob. 13CFU Ch. 15.4 - Prob. 14CFU Ch. 15.4 - Prob. 15E Ch. 15.4 - Prob. 16E Ch. 15.4 - Prob. 17E Ch. 15.4 - Prob. 18E Ch. 15.4 - Prob. 19E Ch. 15.4 - Prob. 20E Ch. 15.4 - Prob. 21E Ch. 15.4 - Prob. 22E Ch. 15.4 - Prob. 23E Ch. 15.4 - Prob. 24E Ch. 15.4 - Prob. 25E Ch. 15.4 - Prob. 26E Ch. 15.4 - Prob. 27E Ch. 15.4 - Prob. 28E Ch. 15.4 - Prob. 29E Ch. 15.4 - Prob. 30E Ch. 15.4 - Prob. 31E Ch. 15.4 - Prob. 32E Ch. 15.4 - Prob. 33E Ch. 15.4 - Prob. 34E Ch. 15.4 - Prob. 35E Ch. 15.4 - Prob. 36E Ch. 15.4 - Prob. 37E Ch. 15.4 - Prob. 38E Ch. 15.4 - Prob. 39E Ch. 15.4 - Prob. 40E Ch. 15.4 - Prob. 41E Ch. 15.4 - Prob. 42E Ch. 15.4 - Prob. 43E Ch. 15.4 - Prob. 44E Ch. 15.4 - Prob. 45E Ch. 15.4 - Prob. 46E Ch. 15.4 - Prob. 47E Ch. 15.4 - Prob. 48E Ch. 15.4 - Prob. 49E Ch. 15.4 - Prob. 50E Ch. 15.4 - Prob. 51E Ch. 15.4 - Prob. 52E Ch. 15.4 - Prob. 53E Ch. 15.4 - Prob. 54E Ch. 15.4 - Prob. 55E Ch. 15.4 - Prob. 56E Ch. 15.4 - Prob. 57E Ch. 15.4 - Prob. 58E Ch. 15.4 - Prob. 59E Ch. 15.4 - Prob. 60E Ch. 15 - Prob. 1SGA Ch. 15 - Prob. 2SGA Ch. 15 - Prob. 3SGA Ch. 15 - Prob. 4SGA Ch. 15 - Prob. 5SGA Ch. 15 - Prob. 6SGA Ch. 15 - Prob. 7SGA Ch. 15 - Prob. 8SGA Ch. 15 - Prob. 9SGA Ch. 15 - Prob. 10SGA Ch. 15 - Prob. 11SGA Ch. 15 - Prob. 12SGA Ch. 15 - Prob. 13SGA Ch. 15 - Prob. 14SGA Ch. 15 - Prob. 15SGA Ch. 15 - Prob. 16SGA Ch. 15 - Prob. 17SGA Ch. 15 - Prob. 18SGA Ch. 15 - Prob. 19SGA Ch. 15 - Prob. 20SGA Ch. 15 - Prob. 21SGA Ch. 15 - Prob. 22SGA Ch. 15 - Prob. 23SGA Ch. 15 - Prob. 24SGA Ch. 15 - Prob. 25SGA Ch. 15 - Prob. 26SGA Ch. 15 - Prob. 27SGA Ch. 15 - Prob. 28SGA Ch. 15 - Prob. 29SGA Ch. 15 - Prob. 30SGA Ch. 15 - Prob. 31SGA Ch. 15 - Prob. 32SGA Ch. 15 - Prob. 33SGA Ch. 15 - Prob. 34SGA Ch. 15 - Prob. 35SGA Ch. 15 - Prob. 36SGA Ch. 15 - Prob. 37SGA Ch. 15 - Prob. 38SGA Ch. 15 - Prob. 39SGA Ch. 15 - Prob. 40SGA Ch. 15 - Prob. 41SGA Ch. 15 - Prob. 42SGA Ch. 15 - Prob. 43SGA Ch. 15 - Prob. 44SGA Ch. 15 - Prob. 45SGA Ch. 15 - Prob. 46SGA Ch. 15 - Prob. 47SGA Ch. 15 - Prob. 48SGA Ch. 15 - 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