10.1 Conics and Calculus 581
10.1 Conics and Calculus
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Match the equation with its graph.
a. d.
b. e.
582 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
c.
____ 2. Match the equation with its graph.
a. d.
b. e.
10.1 Conics and Calculus 583
c.
____ 3. Match the equation with its graph.
a. d.
b. e.
584 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
c.
____ 4. Match the equation with its graph.
a. d.
b. e. none of these
10.1 Conics and Calculus 585
c.
____ 5. Find the vertex of the parabola given by .
a.
b.
c.
d.
e.
____ 6. Find the focus of the parabola given by .
a.
b.
c.
d.
e.
____ 7. Find the directrix of the parabola given by .
a.
b.
c.
d.
e.
586 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 8. Find the vertex, focus, and directrix of the parabola and sketch its graph.
a. vertex: ; focus: ; directrix
x = –1
d. vertex: ; focus: ; directrix
x = 3
b. vertex: ; focus: ; directrix
x = 1
e. vertex: ; focus: ; directrix
x = –1
10.1 Conics and Calculus 587
c.
vertex: ; focus: ; directrix
x = 3
____ 9. Find an equation of the parabola with vertex and directrix .
a.
b.
c.
d.
e.
____ 10. Find the center of the ellipse given by .
a.
b.
c.
d.
e.
____ 11. Find the foci of the ellipse given by .
a.
b.
c.
d.
e.
588 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 12. Find the center, foci, vertices, and eccentricity of the ellipse.
a.
b.
c.
d.
e.
____ 13. Find the eccentricity of the ellipse given by .
a.
b.
c.
d.
e.
____ 14. Find the vertices of the ellipse given by .
a.
b.
c.
d.
e.
10.1 Conics and Calculus 589
____ 15. Find an equation of the ellipse with vertices and eccentricity .
a.
b.
c.
d.
e.
____ 16. Find the center, foci, and vertices of the hyperbola.
a.
b.
c.
d.
e.
590 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 17. Find an equation of the hyperbola with vertices and asymptotes
.
a.
b.
c.
d.
e.
____ 18. Find an equation of the hyperbola with vertices and asymptotes
.
a.
b.
c.
d.
e.
10.1 Conics and Calculus 591
____ 19. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
a. parabola
b. ellipse
c. circle
d. hyperbola
____ 20. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
a. circle
b. hyperbola
c. ellipse
d. parabola
____ 21. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
a. hyperbola
b. circle
c. ellipse
d. parabola
____ 22. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
a. parabola
b. circle
c. ellipse
d. hyperbola
592 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 23. Suppose a church window is bounded above by a parabola and below by the arc of a
circle as shown in figure given below. Find the surface area of the window. Round your answer to
three decimal places.
a. 147.477 ft2
b. 62.143 ft2
c. 81.292 ft2
d. 53.610 ft2
e. 184.590 ft2
____ 24. Suppose a cable of a suspension bridge is suspended (in the shape of a parabola)
between two towers that are 240 meters apart and 40 meters above the roadway as shown in the figure
given below. The cable touches the roadway midway between the towers. Find an equation for the
parabolic shape of cable.
a.
b.
10.1 Conics and Calculus 593
c.
d.
e.
____ 25. Suppose a cable of a suspension bridge is suspended (in the shape of a parabola)
between two towers that are 240 meters apart and 40 meters above the roadway as shown in the figure
given below. The cable touches the roadway midway between the towers. Find the length of the
parabolic supporting cable. Round your answer to two decimal places.
a. 280.79 meters
b. 327.58 meters
c. 291.18 meters
d. 245.71 meters
e. 256.75 meters
____ 26. Uranus moves in an elliptical orbit with the sun at one of the foci. The length of the
half of the major axis is 2,876,769,540 kilometers, and the eccentricity is 0.0444. Find the minimum
distance (perihelion) of Uranus from the sun. Round your answer to nearest kilometer.
a. 3,004,498,108 km
b. 2,749,040,972 km
c. 2,819,234,149 km
d. 127,728,568 km
e. 2,934,304,931 km
____ 27. Earth moves in an elliptical orbit with the sun at one of the foci. The length of the
half of the major axis is 149,598,000 kilometers, and the eccentricity is 0.0167. Find the maximum
distance (aphelion) of Earth from the sun. Round your answer to nearest kilometer.
a. 146,606,040 km
b. 2,498,287 km
c. 152,589,960 km
d. 152,096,287 km
e. 147,099,713 km
594 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
Answer Section
10.1 Conics and Calculus 595