Intermediate Algebra (11th edition)

CHAPTER 11 Review Exercises 673

26.Ships and planes often use a location-
finding system called LORAN. With this
system, a radio transmitter at Msends out
a series of pulses. When each pulse is
received at transmitter S, it then sends out a
pulse. A ship at Preceives pulses from
both Mand S. A receiver on the ship meas-
ures the difference in the arrival times of
the pulses. A special map gives hyperbolas that correspond to the differences in arrival
times (which give the distances and in the figure.) The ship can then be located as ly-
ing on a branch of a particular hyperbola.
Suppose mi and mi, and the distance between transmitters Mand
Sis 100 mi. Use the definition to find an equation of the hyperbola on which the ship is
located.

11.4 Solve each system.

d 1 = 80 d 2 = 30

d 1 d 2

M S

d 1 P

d 2

27. 28.

y+ 2 x= 4

y+ 1 =x^2 + 2 x

x+ 2 y=- 12

2 y= 3 x-x^2

29. 30.

x- 2 y= 6

xy= 8

y-x=- 2

x^2 + 3 y^2 = 28

31. 32.

x^2 + 4 y^2 = 18

3 x^2 - 2 y^2 = 12

x^2 - 2 y^2 =- 6

x^2 + y^2 = 6

33.Concept Check How many solutions are possible for a system of two equations whose
graphs are a circle and a line?

34.Concept Check How many solutions are possible for a system of two equations whose
graphs are a parabola and a hyperbola?

11.5 Graph each inequality.

35. 36. 37.

Graph each system of inequalities.

9 x^2 Ú 16 y^2 + 144 4 x^2 +y^2 Ú 16 y6- 1 x+ 222 + 1

38. 39. 40.

x^2 +y^2 ... 16

9 x^2 ... 4 y^2 + 36

4 x^2 + 9 y^2 ... 36

|y| 71

|x|... 2

3 x- y... 6

2 x+ 5 y... 10

MIXED REVIEW EXERCISES

Graph.

x^2616 - y^2

ƒ 1 x 2 = 24 - x 4 y 73 x- 12

x^2 + 9 y^2 = 9 x^2 - 9 y^2 = 9

x^2 +y^2 = 25

y^2

4

- 1 =

x^2

9