Deck 10: Section 2: Conics, Parametric Equations, and Polar Coordinates

Question 1

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

Answer 1

smooth everywhere

Question 2

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

Answer 2

none of the above

Question 3

Sketch the curve represented by the parametric equations .

A)
B)
C)
D)
E)

Answer 3

Question 4

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

A)
B)
C)
D)
E)

Question 5

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

A)
B)
C)
D)
E)

Question 6

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 7

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

A)
B)
C)
D)
E)

Question 8

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 and . 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 and . Round your answer to one decimal place.

A)
B)
C)
D)
E)

Question 9

Find a set of parametric equations for the rectangular equation .

A)
B)
C)
D)
E)

Question 10

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

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

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

A)
B)
C)
D)
E)

Question 13

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

A)
B)
C)
D)
E)

Question 14

Sketch the curve represented by the parametric equations .

A)
B)
C)
D)
E)

Question 15

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 and . 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 16

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)

Question 17

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