Larson_Calculus_10e ch10sec02
MULTIPLE CHOICE
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.
c.
3. Write the corresponding rectangular equation for the curve represented by the parametric equations
by eliminating the parameter.
a.
b.
c.
d.
e.
4. Sketch the curve represented by the parametric equations .
a.
d.
b.
e.
c.
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
c.
7. Sketch the curve represented by the parametric equations, and write the corresponding rectangular
equation by eliminating the parameter.
a.
d.
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.
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.
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
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.
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.