BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.8, Problem 91E
To determine

To calculate: Thecenter and radius of the circle (x+3)2+(y4)2=25 and sketch the graph of the circle.

Expert Solution

Answer to Problem 91E

The center of the circle is (3,4) and radius is 5 units. The graph of the circle is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 91E , additional homework tip  1

Explanation of Solution

Given information:

The equation (x+3)2+(y4)2=25 .

Formula used:

The standard form of the equation of the circle is (xh)2+(yk)2=r2 , where (h,k) denote the center of the circle and r denote the radius.

Calculation:

Consider the equation (x+3)2+(y4)2=25 .

Rewrite the equation as,

  (x(3))2+(y4)2=52

Recall that the standard form of the equation of the circle is (xh)2+(yk)2=r2 , where (h,k) denote the center of the circle and r denote the radius.

Compare, (xh)2+(yk)2=r2 and (x(3))2+(y4)2=52 .

Here, h=3,k=4 and r=5 .

Therefore, center of circle is (3,4) and radius is 5 .

Now, on the Cartesian plane construct a circle with center at (3,4) and radius 5 units.

The graph obtained is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 91E , additional homework tip  2

Thus, the center of the circle is (3,4) and radius is 5 units.

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