BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter B, Problem 39E
To determine

To calculate: To show that the equation represents the circle and then find the center and radius of circle

Expert Solution

Answer to Problem 39E

Equation is equation of circle. Also center of circle is (2,5) and radius of circle is 4

Explanation of Solution

Given information: Equation is x2+y24x+10y+13=0

Formula Used:

Equation of circle with center as (h,k) and radius r is given as

  (xh)2+(yk)2=r2

Calculation:

Equation is given as follows:

  x2+y24x+10y+13=0

Rearranging the terms of equation,

  x24x+y2+10y+13=0(x24x+4)+(y2+10y+25)+13=4+25(x2)2+(y+5)2=2913(x2)2+(y(5))2=16(x2)2+(y(5))2=42

Comparing the above equation with standard equation of circle (xh)2+(yk)2=r2 ,

  Centre,(h,k)=(2,5)Radius,r=4

Conclusion:

Hence, given equation is equation of circle. Also center of circle is (2,5) and radius of circle is 4

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