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10.1 Conics and Calculus
608
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.
609 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
610
c.
____ 3. Match the equation with its graph.
a. d.
b. e.
611 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
612
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.
613 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: ; d. vertex: ; focus: ; directrix
directrix x = –1 x = 3
b. vertex: ; focus: ; directrix e. vertex: ; focus: ;
x = 1 directrix x = –1
10.1 Conics and Calculus
614
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.
615 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
616
____
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.
617 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
618
____ 19.
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
parabola
ellipse
circle
hyperbola
____ 20. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
circle
hyperbola
ellipse
parabola
____ 21. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
hyperbola
circle
ellipse
parabola
____ 22. Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
parabola
circle
ellipse
hyperbola
619
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.
147.477 ft2
62.143 ft2
81.292 ft2
53.610 ft2
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
620
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.
280.79 meters
327.58 meters
291.18 meters
245.71 meters
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.
3,004,498,108 km
2,749,040,972 km
2,819,234,149 km
127,728,568 km
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.
146,606,040 km
2,498,287 km
152,589,960 km
152,096,287 km
147,099,713 km
621 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
Answer Section
10.1 Conics and Calculus
622
623 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
10.2 Plane Curves and Parametric Equations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1.
Write the corresponding rectangular equation for the curve represented by the
parametric equation
by eliminating the parameter.
a.
b.
c.
d.
e.
____ 2. Sketch the curve represented by the parametric equations .
a. d.
b. e.
10.2 Plane Curves and Parametric Equations
624
c.
____ 3.
Write the corresponding rectangular equation for the curve represented by the
parametric equations
by eliminating the parameter.
a.
b.
c.
d.
e.
625 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 4. Sketch the curve represented by the parametric equations .
a. d.
b. e.
c.
10.2 Plane Curves and Parametric Equations
626
____ 5.
Write the corresponding rectangular equation for the curve represented by the
parametric equations
by eliminating the parameter.
a.
b.
c.
d.
e.
____ 6. Sketch the curve represented by the parametric equations, and write the
corresponding rectangular equation by eliminating the parameter.
a. d.
b. e. none of the above
627 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
c.
____ 7. Sketch the curve represented by the parametric equations, and write the
corresponding rectangular equation by eliminating the parameter.
a. d.
