Deck 10: Conics and Calculus

Question 1

an equation of the hyperbola with vertices

Answer 1

C

Question 2

the center, foci, vertices, and eccentricity of the ellipse.

Answer 2

E

Question 3

an equation of the ellipse with vertices

Answer 3

D

Question 4

the focus of the parabola given by

Question 5

Question 6

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Question 7

Match the equation with its graph.

Question 8

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Question 9

the center of the ellipse given by

Question 10

the vertices of the ellipse given by

Question 11

Match the equation with its graph.

Question 12

the vertex, focus, and directrix of the parabola and sketch its graph.

Question 13

Match the equation with its graph.

Question 14

the foci of the ellipse given by

Question 15

the directrix of the parabola given by

Question 16

the vertex of the parabola given by

Question 17

Question 18

Match the equation with its graph.

Question 19

the eccentricity of the ellipse given by

Question 20

the center, foci, and vertices of the hyperbola.

Question 21

the result, "the set of parametric equations for the ellipse is

Question 22

the result, "the set of parametric equations for the circle is

Question 23

a set of parametric equations for the rectangular equation

Question 24

Sketch the curve represented by the parametric equations

Question 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.

Question 26

the result, "the set of parametric equations for the line passing through

Question 27

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Question 28

Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter.

Question 29

Write the corresponding rectangular equation for the curve represented by the parametric equation by eliminating the parameter.

Question 30

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.

Question 31

Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter.

Question 32

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

Question 33

a set of parametric equations for the rectangular equation

Question 34

Sketch the curve represented by the parametric equations

Question 35

a set of parametric equations for the rectangular equation

Question 36

Write the corresponding rectangular equation for the curve represented by the parametric equations

Question 37

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

Question 38

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.

Question 39

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.

Question 40

Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter.

Question 41

the arc length of the curve on the given interval.

Question 42

the arc length of the curve your answer to three decimal places.

A)287.453
B)191.635
C)193.606
D)66.480
E)99.721

Question 43

Question 44

Question 45

the arc length of the curve on the given interval.

Question 46

Question 47

Round your answer to two decimal places, if necessary.

Question 48

the arc length of the curve on the given interval.

Question 49

point corresponding to t = 5.

Question 50

or concave upward.

Question 51

parametric equations for the path of a projectile launched at a height h feet above

Question 52

Question 53

Question 54

Determine the t intervals on which the curve downward or concave upward.

Question 55

Question 56

Identify any points at which the Folium of Descartes smooth. Round your answer to two decimal places, if necessary.

Question 57

parametric equations for the path of a projectile launched at a height h feet above

Question 58

all points (if any) of horizontal and vertical tangency to the curve

Question 59

all points (if any) of horizontal and vertical tangency to the curve

Question 60

Question 61

Round your answer to two decimal places, if necessary.

Question 62

Question 63

the arc length of the curve your answer to three decimal places.

A)287.453
B)191.635
C)193.606
D)66.480
E)99.721

Question 64

Question 65

all points (if any) of horizontal and vertical tangency to the curve

Question 66

the area of the surface generated by revolving the curve about the given axis.

Question 67

the area of the surface generated by revolving the curve

Question 68

Determine the t intervals on which the curve or concave upward.

Question 69

the arc length of the curve on the given interval.

Question 70

an equation of the tangent line at a point

Question 71

Question 72

all points (if any) of horizontal and vertical tangency to the curve

Question 73

path of a projectile is modeled by the parametric equations

Question 74

Determine the t intervals on which the curve downward or concave upward.

Question 75

the arc length of the curve on the given interval.

Question 76

point corresponding to t = 5.

Question 77

the area of the surface generated by revolving the curve about the given axis.

Question 78

the arc length of the curve on the given interval.

Question 79

Question 80