Intermediate Algebra (11th edition)

SECTION 11.2 The Circle and the Ellipse 647

Complete solution available
on the Video Resources on DVD

11.2 EXERCISES

1. See Example 1.Consider the circle whose equation is.
   (a)What are the coordinates of its center? (b) What is its radius?
   (c)Sketch its graph.
   2.Why does a set of points defined by a circle notsatisfy the definition of a function?

Concept Check Match each equation with the correct graph.

3. A. B.

4.

5. C. D.

6.

Find the equation of a circle satisfying the given conditions. See Examples 2 and 3.

7.Center: ; radius: 2 8.Center: ; radius: 4

9.Center: ; radius: 10.Center: ; radius:

Find the center and radius of each circle. ( Hint: In Exercises 15 and 16, divide each side by a

common factor.) See Example 4.

Graph each circle. Identify the center if it is not at the origin. See Examples 1, 2, and 4.

25.x^2 +y^2 + 6 x- 6 y+ 9 = 0 26.x^2 +y^2 - 4 x+ 10 y+ 20 = 0

x^2 +y^2 - 4 x- 6 y+ 9 = 0 x^2 +y^2 + 8 x+ 2 y- 8 = 0

1 x+ 322 + 1 y- 222 = 9 1 x- 122 + 1 y+ 322 = 16

2 y^2 = 10 - 2 x^23 x^2 = 48 - 3 y^2

x^2 +y^2 = 9 x^2 +y^2 = 4

3 x^2 + 3 y^2 - 12 x- 24 y+ 12 = 0 2 x^2 + 2 y^2 + 20 x+ 16 y+ 10 = 0

x^2 +y^2 + 10 x- 14 y- 7 = 0 x^2 +y^2 - 2 x+ 4 y- 4 = 0

x^2 +y^2 + 4 x+ 6 y+ 9 = 0 x^2 +y^2 - 8 x- 12 y+ 3 = 0

1 - 8, - 52 25 1 - 12, 13 2 27

1 - 4, 3 2 1 5, - 22

1 x+ 322 + 1 y+ 222 = 25

1 x+ 322 + 1 y- 222 = 25

1 x- 322 + 1 y+ 222 = 25

1 x- 322 + 1 y- 222 = 25

x^2 +y^2 = 25

x

y

–3 0

–2

x

y

0 3

2

x

y

0 3

–2

x

y

–3 0

2

27.A circle can be drawn on a piece of posterboard by fastening

one end of a string with a thumbtack, pulling the string taut

with a pencil, and tracing a curve, as shown in the figure.

Explain why this method works.