Page 9 - For Okta_Float

Applications 43. Sports Cindy is taking an archery class and decides
and Problem to practice her skills at home. She attaches the target
Solving shown at right to a bale of hay. The circles on the
A 24 in.
target are concentric and equally spaced apart.
B
Real World
a. If the common center of the circles is located at the
Application C
origin, write an equation that models the largest
circle. 24 in.
b. If the smallest circle is modeled by the equation
2
2
x y 6.25, find the area of the region marked B.
44. Geometry Write the equation of a circle that circumscribes the triangle whose
sides are the graphs of 4x 7y 27, x 5y 3 0, and 2x 3y 7 0.
45. Critical Thinking Consider a family of circles in which h k and the radius
is 2. Let k be any real number.
Look Back
Refer to Lesson 3-2 a. Write the equation of the family of circles.
to review families of b. Graph three members of this family on the same set of axes.
graphs.
c. Write a description of all members of this family of circles.
46. Transportation A moving truck 7 feet
wide and 13 feet high is approaching a
semi-circular brick archway at an
apartment complex. The base of the
archway is 28 feet wide. The road under 14 feet
the archway is divided, allowing for
two-way traffic. 28 feet
a. Write an equation, centered at the
origin, of the archway that models
its shape.
b. If the truck remains just to the right of the median, will it be able to pass
under the archway without damage? Explain.
47. Critical Thinking Find the radius and the coordinates of the center of a circle
2
2
defined by the equation x y 8x 6y 25 0. Describe the graph of
this circle.
48. Agriculture One method of
irrigating crops is called the center
pivot system. This system rotates
a sprinkler pipe from the center
of the field to be irrigated. Suppose
a farmer places one of these units
at the center of a square plot of
land 2500 feet on each side. With
the center of this plot at the origin,
the irrigator sends out water far
enough to reach a point located
at (475, 1140).
a. Find an equation representing the farthest points the water can reach.
b. Find the area of the land that receives water directly.
c. About what percent of the farmer’s plot does not receive water directly?
49. Critical Thinking Consider points A(3, 4), B(3, 4), and P(x, y).
a. Write an equation for all x and y for which P A ⊥ P B .
b. What is the relationship between points A, B, and P if P A ⊥ P B ?

Lesson 10-2 Circles 629