596 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 597
c.
____ 3. Write the corresponding rectangular equation for the curve represented by the
parametric equations by eliminating the parameter.
a.
b.
c.
d.
e.
598 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 599
____ 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
600 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.
10.2 Plane Curves and Parametric Equations 601
b.
e.
c.
____ 8. 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.
602 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 9. 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.
____ 10. 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.
____ 11. Find a set of parametric equations for the rectangular equation .
a.
b.
c.
d.
e.
____ 12. Find a set of parametric equations for the rectangular equation that
satisfies the condition at the point .
a.
b.
c.
d.
e.
10.2 Plane Curves and Parametric Equations 603
____ 13. Find a set of parametric equations for the rectangular equation that satisfies
the condition at the point .
a.
b.
c.
d.
e.
____ 14. 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
____ 15. 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
604 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
____ 16. 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.
10.2 Plane Curves and Parametric Equations 605
____ 17. 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.
606 Chapter 10: Conics, Parametric Equations, and Polar Coordinates
10.2 Plane Curves and Parametric Equations
Answer Section