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 10.2, Problem 44E

To determine

To write: The equation of circle of the given details.

Expert Solution & Answer

Answer to Problem 44E

(x−132)2+(y−92)2=652

Explanation of Solution

Given information: Geometry: A circle that circumscribes the triangle whose sides are the graphs of 4x−7y=27,x−5y+3=0 and 2x+3y−7=0 .

Calculation:

If you graph the lines, you need to find the points of intersection. This is the first step.

You can solve them with the calculator, substitution or elimination. This gives you 3 points that the circle passes through.

From here this problem is similar to problems solved earlier.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.2, Problem 44E , additional homework tip 1

Points (x,y):(2,1),(5,−1),(12,3)

Plug in the 3 points to create 3 equations which we can use to solve the system to find all of the missing values.

Remember the form:

(x−h)2+(y−k)2=r2Vertex at:(h,k)

Pt:(2,1):(2−h)2+(1−k)2=r2h2+k2−4h−2k+5=r2Pt:(5,−1):(5−h)2+(−1−k)2=r2h2+k2−10h+2k+26=r2Pt:(12,3):(12−h)2+(3−k)2=r2h2+k2−24h−6k+153=r2

Set 1^s^t 2 equations equal to each other: because they both equal r2 .

h2+k2−4h−2k+5=h2+k2−10h+2k+266h=4k+21→h=4k+216

Set the 1^s^t and 3^r^d equations equal: because they also both equal r2 .

h2+k2−4h−2k+5=h2+k2−24h−6k+15320h=−4k+148=−4k−14820

Set the 2 equations for h equal to find k .

−4k−14820=4k+216→k=92This means:h=4(92)+216=132

Plug these values for h and k into any of the equations to find r .

(132)2+(92)2−4(132)−2(92)+5=r2r2=652

Final equation is:

(x−132)2+(y−92)2=652

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.2, Problem 44E , additional homework tip 2

Chapter 10.2, Problem 43E

Chapter 10.2, Problem 45E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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