To write: The standard form of the equation of the circle that passes through the points with the coordinates (4,5),(−2,3),(−4,−3) . Then identify the center and radius.

Expert Solution & Answer

Answer to Problem 32E

(x+2)2+(y−3)2=50r=50Center(−2,3)

Explanation of Solution

Given information: The coordinates (4,5),(−2,3),(−4,−3)

Calculation:

Points (x,y):(4,5),(−2,3),(−4,−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:(4,5):(4−h)2+(5−k)2=r2h2+k2−10h−8k+41=r2Pt:(−2,3):(−2−h)2+(3−k)2=r2h2+k2−6h+4k+13=r2Pt:(−4,−3):(−4−h)2+(−3−k)2=r2h2+k2+6h+8k+25=r2

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

h2+k2−10h−8k+41=h2+k2−6h+4k+13h=−3k+7

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

h2+k2−10h−8k+41=h2+k2+6k+8k+25h=−k+1

Set these 2 results equal because they both equal r²

−k+1=−3k+7→k=3→h=−2

You know the center (h,k)=(−2,3)

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

(−2)2+(3)2−10(−2)−8(3)+41=r2r2=50

Standard form:

(x+2)2+(y−3)2=50r=50Center(−2,3)

Chapter 10.2, Problem 31E

Chapter 10.2, Problem 33E

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

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