Deck 10: Conics, Parametric Equations, and Polar Coordinates

Question 1

Match the equation with its graph.

A)
B)
C)
D)
E)none of these

Answer 1

none of these

Question 2

Find the directrix of the parabola given by

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the eccentricity of the ellipse given by

A)
B)
C)
D)
E)

Answer 3

Question 4

Sketch the curve represented by the parametric equations

A)
B)
C)
D)
E)

Question 5

Find the focus of the parabola given by

A)
B)
C)
D)
E)

Question 6

Find the vertex of the parabola given by

A)
B)
C)
D)
E)

Question 7

Match the equation with its graph.

A)
B)
C)
D)
E)

Question 8

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

A)
B)
C)
D)
E)

Question 9

Sketch the curve represented by the parametric equations

A)
B)
C)
D)
E)

Question 10

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

A)
B)
C)
D)
E)

Question 11

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

A)
B)
C)
D)
E)

Question 12

Find an equation of the parabola with vertex and directrix

A)
B)
C)
D)
E)

Question 13

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

A)
B)
C)
D)
E)none of the above

Question 14

Find the center of the ellipse given by

A)
B)
C)
D)
E)

Question 15

Find the foci of the ellipse given by

A)
B)
C)
D)
E)

Question 16

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

A)vertex: ; focus: directrix
B)vertex: ; focus: directrix
C)vertex: focus: directrix x = 3
D)vertex: ; focus: directrix x = -1 x = 3
E)vertex: ; focus: directrix x = 1 x = -1

Question 17

Match the equation with its graph.

A)
B)
C)
D)
E)

Question 18

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

A)
B)
C)
D)
E)

Question 19

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

A)
B)
C)
D)
E)

Question 20

Match the equation with its graph.

A)
B)
C)
D)
E)

Question 21

The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is
Given by .The center field fence in a ballpark is feet
High and feet from home plate.The ball is hit 2 feet above the ground.It leaves the bat at an angle
Of degrees with the horizontal at a speed of 100 miles per hour as shown in the figure.Write a set
Of parametric equations for the path of the ball.

A)
B)
C)
D)
E)

Question 22

Identify any points at which the Folium of Descartes is not smooth.Round your answer to two decimal places, if necessary.

A)not smooth when
B)not smooth when
C)not smooth when
D)smooth everywhere
E)not smooth when

Question 23

Find a set of parametric equations for the rectangular equation that satisfies the condition at the point

A)
B)
C)
D)
E)

Question 24

Use the result, "the set of parametric equations for the line passing through and to find a set of parametric equations for the line passing through

A)
B)
C)
D)
E)

Question 25

Identify any points at which the cycloid is not smooth.

A)not smooth when
B)smooth everywhere
C)not smooth when
D)not smooth when
E)not smooth when

Question 26

Find a set of parametric equations for the rectangular equation that satisfies the condition at the point

A)
B)
C)
D)
E)

Question 27

The parametric equations for the path of a projectile launched at a height feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is
Given by The center field fence in a ballpark is feet
High and feet from home plate.The ball is hit 3 feet above the ground.It leaves the bat at an angle
Of degrees with the horizontal at a speed of 100 miles per hour as shown in the figure.Find the
Minimum angle at which the ball must leave the bat in order for the hit to be a home run using the
Parametric equations Round your answer to one
Decimal place.

A)
B)
C)
D)
E)

Question 28

Use the result, "the set of parametric equations for the circle is to find a set of parametric equations for the circle with a center and radius

A)
B)
C)
D)
E)

Question 29

Find a set of parametric equations for the rectangular equation

A)
B)
C)
D)
E)

Question 30

Use the result, "the set of parametric equations for the ellipse is to find a set of parametric equations for the ellipse with vertices and and with foci at and

A)
B)
C)
D)
E)