Math 152B Practice Exam 4: Chapter 10

1. Graph the parabola using the following steps: x = -y^ + -15 a. Write the parabola in vertex form.

"b. l)etermme the directioojOlMdiich it opens.

c. Find the vertex^ ~

d. Find the y-intercept(s). ^

e. Find the x-intercept(s). \ J ^ i f ^ ^ A c ^ M

the graph 2. Find the equation of the graph

(4, 5)

3. Write the circle in standard form and graph: .r + >'^-6jc + 14>' + 33 = 0

1

4. Find the equation of the graph.

5. Given the following diagram, a. Find the midpoint of the circle (-6.7)

b. Find the distance of the radius of the circle.

c. Find the equation of the circle.

6. Write the ellipse in standard form and graph; 16x^ + 9} ^ - 96x + 36>' + 36 = 0

7. Find the equation of the graph.

A,

J

-5

- U

5 . V

( I . - 3 )

H

3fc

8. Find how far the focus points are from the center of the ellipse.

9. A semi-elliptic archway has aHeight of 10 feet and a width of 40 feet as shown in the figure below. If you pictured a completed ellipse with the center of the ellipse being at the center of the road, determine the equation of the ellipse.

40 tl

. 3 ~~zo Hoc I 10. Find the equation of the ellipse if (4,4) and (4, -6) are the endppints of the major axisjind (0, -1) and

(8, -1) are the endpoints of the minor axis.

11. Write the hyperbola in standard form and graph: 36y - 9x = 324

3 6 ' f ' 6 z

12. Find the equation of this graph.

13. Determine an equation of the hyperbola whose vertices are (0, 12) and (0,-12) and whose asymptotes are 3 . 3

y = —xanay =

X y 14. Determine the domain and range of the hyperbola whose eauation ' S T T - — = 1 •

1 - t 49 81

15. Determine if the equation represents a parabola, circle, ellipse, or hyperbola.

a. x ^ + 9 / = 3 6 J^^^^s^ tW pt b. y~-x + 2y = 9

c

d. 3 y = 7 -

34-

5 16. Solve the system , / _ i

17. Solve the system

JJC^+/-2JC + 4>' = 0

I. Solve me system ^

x = z

\,>lu^C^^3^=c ^ ^ ^ ^ =-3

19. Solve the system 4JC2-9/ = 36

" 5;c-6>' = 0

20. A system for tracking ships indicates that a ship Hes on a hyperbolic path described hy2x~ -y^ = 1. The

process is repeated and the ship is found to lie on a hyperbolic path described by 2y^ -x~ = \. If it is known that the ship is located in the first quadrant of the coordinate system, determine its exact location.

21. The cost, C, of manufacturing and selling .)^ni ts of a product is C = 22x - 7, and the corresponding revenue, R,isR = x"^ -55 . Find the break-even value oix.

C-.52I ^=521

22. Given two whole numbers, x and y: tU -Zs X'-5( \\tir product of the two numbers, added to the smallest, is 70. Three times the smallest plus twice the u _ \ - i t ^ largest is 41. Find the two numbers. , -4

Z 3

23. A right triangle has a perimeter of 30 inches and an area of 30 square inches. Find the lengths of its

/

sides.

24. The area of a rectangle is 85 square feet and the perimeter is 37 feet. Find the dimensions of the

XM,= :> 4=% r^2)^^'^-6\^^ >6=5S.a' 5

25. A rectangle has an area of 60 square feet, and the diagonal across the rectangle measures 13 feet. Find the dimensions of the rectangle.

X - 5