Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
Stewart_Calc_7ET ch10sec06
MULTIPLE CHOICE
1. Write a polar equation in r and
of an ellipse with the focus at the origin, with the eccentricity
and directrix .
a.
b.
c.
d.
e.
2. The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity and
one focus at the Sun. The length of its major axis is AU. [An astronomical unit (AU) is
the mean distance between Earth and the Sun, about 93 million miles.] Find the maximum
distance from the comet to the Sun. (The perihelion distance from a planet to the Sun is
and the aphelion distance is .) Find the answer in AU and round to the
nearest hundredth.
a.
AU
b.
AU
c.
AU
d.
AU
e.
AU
3. Write a polar equation in r and of an ellipse with the focus at the origin, with the eccentricity
and vertex at .
a.
b.
c.
d.
e.
4. Write a polar equation of the conic that has a focus at the origin, eccentricity , and directrix
. Identify the conic.
a.
, hyperbola
b.
, hyperbola
c.
, ellipse
d.
, ellipse
5. Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at
one focus. Its perihelion distance (minimum distance from the planet to the sun) is
approximately 1.3 km, and its aphelion distance (maximum distance from the planet to
the sun) is approximately 6.9 km. Approximate the eccentricity of the planet’s orbit.
Round to three decimal places.
a.
0.683
b.
5.308
c.
1.464
d.
0.188
3
2
6. Find the equation of the directrix of the conic.
a.
b.
c.
d.
e.
7. The planet Mercury travels in an elliptical orbit with eccentricity . Its minimum distance
from the Sun is km. If the perihelion distance from a planet to the Sun is
and the aphelion distance is , find the maximum distance (in km) from Mercury to
the Sun.
a.
km
b.
km
c.
km
d.
km
e.
km
8. Write a polar equation in r and of a hyperbola with the focus at the origin, with the eccentricity
and directrix .
a.
b.
c.
d.
e.
9. Find the eccentricity of the conic.
a.
b.
c.
d.
e.
SHORT ANSWER
1. Consider the polar equation .
(a) Find the eccentricity and an equation of the directrix of the conic.
(b) Identify the conic.
(c) Sketch the curve.
2. Consider the polar equation .
(a) Find the eccentricity and an equation of the directrix of the conic.
(b) Identify the conic.
(c) Sketch the curve.
3. Consider the polar equation .
(a) Find the eccentricity and an equation of the directrix of the conic.
(b) Identify the conic.
(c) Sketch the curve.
