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The circle or ellipse shown in the calculator-generated graph was created

Question : The circle or ellipse shown in the calculator-generated graph was created : 2151704

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions y1 and y2 that were used to obtain the graph whose equation is given?

1) x2 + y2 = 25

A) y1 = √(25 + x2), y2 = - √(25 - x2)

B) y1 = √(x2 - 25), y2 = - √(x2 - 25)

C) y1 = √(25 - x2), y2 = - √(25 - x2)

D) y1 = √(25 - x2), y2 = √(25 + x2)

2) (x2/25) + (y2/25) = 1

A) y1 = √(5 + x2), y2 = - √(5 + x2)

B) y1 = √(25 + x2), y2 = - √(25 + x2)

C) y1 = √(5 - x2), y2 = - √(5 - x2)

D) y1 = √(25 - x2), y2 = - √(25 - x2)

3) (x2/16) + (y2/25) = 1

A) y1 = 5√(1 - (x2/4)), y2 = -5√(1 - (x2/4))

B) y1 = 5√(1 - (x2/16)), y2 = -5√(1 - (x2/16))

C) y1 = 5√(1 + (x2/16)), y2 = -5√(1 + (x2/16))

D) y1 = 5√(1 - (x/4)), y2 = -5√(1 - (x/4))

4) (x - 5)2 + y2 = 25

A) y1 = 25 + √(x - 5), y2 = 25 - √(x - 5)

B) y1 = √(25 - (x - 5)2), y2 = - √(25 - (x - 5)2)

C) y1 = 5 + √(x - 5), y2 = 5 - √(x - 5)

D) y1 = √(25 + (x - 5)2), y2 = - √(25 + (x - 5)2)

5) (x - 1)2 + (y - 1)2 = 1

A) y1 = -1 + √(1 - (x - 1)2), y2 = 1 - √(1 - (x - 1)2)

B) y1 = -1 + √(1 - (x - 1)2), y2 = -1 - √(1 - (x - 1)2)

C) y1 = 1 + √(1 - (x - 1)2), y2 = 1 - √(1 - (x - 1)2)

D) y1 = 1 + √(1 - (x - 1)2), y2 = -1 - √(1 - (x - 1)2)

6) (x - 2)2 + (y - 2)2 = 1

A) y1 = 2 + √(1 - (x - 2)2), y2 = 2 - √(1 - (x - 2)2)

B) y1 = 2 + √((x - 2)2 - 1), y2 = 2 - √((x - 2)2 - 1)

C) y1 = √(1 - (x - 2)2), y2 = - √(1 - (x - 2)2)

D) y1 = 2 + √(1 + (x - 2)2), y2 = 2 - √(1 + (x - 2)2)

7) x2 + ((y + 5)2/25) = 1

A) y1 = -5 + 5√(1 - x2), y2 = -5 - 5√(1 - x2)

B) y1 = -5 + 5√(1 + x2), y2 = -5 - 5√(1 + x2)

C) y1 = 5 + 5√(1 + x2), y2 = 5 - 5√(1 + x2)

D) y1 = 5 + 5√(1 - x2), y2 = 5 - 5√(1 - x2)

Solve the problem.

8) An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 6 mi. Find an equation for the ellipse, where x and y are measured in mi, if the path is to touch the center of the property line on all 4 sides.

 

                                       6 mi

A) (x2/ 9) + (y2/ 25) = 1

B) (x2/ 25) + (y2/ 6) = 1

C) (x2/ 9) + (y2/100) = 1

D) (x2/100) + (y2/ 9) = 1

9) A railroad tunnel has the shape of half an ellipse. The height of the tunnel at the center is 50 ft and the vertical clearance must be 25 ft at a point 21 ft from the center. Find an equation for the ellipse, where x and y are measured in ft.

A) (x2/ 2,500) + (y2/ 588) = 1

B) (x2/ 588) + (y2/ 2,500) = 1

C) (x2/441) + (y2/ 2,500) = 1

D) (x2/ 588) + (y2/ 625) = 1

10) A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius 787 km. Determine an equation for the ellipse, where x and y are measured in km, if the distance of the satellite from the surface of the moon varies from 446 km to 154 km.

A) (x2/4462) + (y2/1542) = 1

B) (x2/1,233) +x (y2/941) = 1

C) (x2/  9412) + (y2/ 1,2332) = 1

D) (x2/ 154) + (y2/ 446) = 1

11) A rectangular board is 2 by 10. How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

A) 4.0

B) 1.0

C) .1

D) 4.9

12) A rectangular board is 3 by 18. The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.

A) 36

B) 18

C) 3

D) 6

Decide whether the statement is true or false.

13) The circle with equation x2 + y2 = 64 has center at (8, 8).

A) True

B) False

14) The circle with equation (x + 1)2 + (y - 1)2 = 4 has center at (1, -1).

A) True

B) False

15) The equation of a circle centered at the origin with radius 3 is x2 + y2 = 3.

A) True

B) False

16) The equation of a semicircle that is the upper half of the circle centered at the origin with radius 7 is y = √(49 - x2).

A) True

B) False

17) The x-intercepts of the ellipse with equation (x2/64) + (y2/36) = 1 are (8, 0) and (-8, 0).

A) True

B) False

18) The y-intercepts of the ellipse with equation (x2/25) + (y2/16) = 1 are (0, 5) and (0, -5).

A) True

B) False

19) The y-intercepts of the ellipse with equation (x2/36) + (y2/4) = 1 are (0, 4) and (0, -4).

A) True

B) False

20) The graph of the equation (x/64) + (y/4) = 1 is an ellipse.

A) True

B) False

Solution
5 (1 Ratings )

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Algebra 4 Months Ago 41 Views
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