Stewart_Calc_7ET ch10sec05
MULTIPLE CHOICE
1. Find an equation for the conic that satisfies the given conditions.
parabola, vertex (0, 0), focus (0, –)
a.
b.
c.
d.
e.
2. Find an equation for the conic that satisfies the given conditions.
hyperbola, foci (0, ± ) , vertices (0, ± )
a.
b.
c.
d.
e.
3. Find an equation of the hyperbola centered at the origin that satisfies the given condition.
Vertices: (± 4, 0), asymptotes: y = ± x
a.
7
4
b.
c.
d.
4. Find an equation of the parabola with focus and directrix .
a.
b.
c.
d.
e.
5. Find an equation of the hyperbola with vertices and asymptotes .
a.
b.
c.
d.
e.
6. Find an equation for the conic that satisfies the given conditions.
ellipse, foci , length of major axis 8
a.
b.
c.
d.
e.
7. In the LORAN (LOng RAnge Navigation) radio navigation system, two radio stations
located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The
onboard computer converts the time difference in receiving these signals into a distance
difference , and this, according to the definition of a hyperbola, locates the ship or
aircraft on one branch of a hyperbola (see the figure). Suppose that station B is located L =
mi due east of station A on a coastline. A ship received the signal from B
microseconds (µs) before it received the signal from A. Assuming that radio signals travel at
a speed of ft /µs and if the ship is due north of B, how far off the coastline is the ship?
Round your answer to the nearest mile.
a.
miles
b.
miles
c.
miles
d.
miles
e.
miles
8. Match the equation with the correct graph.
a.
c.
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 x
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
–7
–8
y
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 x
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
–7
–8
y
b.
d.
9. Find an equation of the ellipse that satisfies the given conditions.
Foci: (0, ± 1), vertices (0, ± 6)
a.
b.
c.
d.
10. Find an equation of the ellipse that satisfies the given conditions.
Foci: (0, ± 8), vertices (0, ± 9)
a.
b.
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 x
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
–7
–8
y
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 x
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
–7
–8
y
c.
d.
MULTIPLE RESPONSE
1. A cross-section of a parabolic reflector is shown in the figure. The bulb is located at the
focus and the opening at the focus is 18 cm. Find an equation of the parabola. Let V be the
origin. Find the diameter of the opening |CD| , 19 cm from the vertex.
a.
b.
c.
The equation is
d.
e.
The equation is
f.
The equation is
2. Find the vertices, foci and asymptotes of the hyperbola.
a.
The foci are
b.
The vertices are (4 , 5)
c.
The foci are
d.
The vertices are
e.
The asymptote is
f.
The asymptotes are
NUMERIC RESPONSE
1. The point in a lunar orbit nearest the surface of the moon is called perilune and the point
farthest from the surface is called apolune. The Apollo 11 spacecraft was placed in an
elliptical lunar orbit with perilune altitude km and apolune altitude km (above the
moon). Find an equation of this ellipse if the radius of the moon is km and the center
of the moon is at one focus.
SHORT ANSWER
1. Find the vertices, foci, and asymptotes of the hyperbola.
2. Find the vertex, focus, and directrix of the parabola.
5
3. Find the vertex, focus, and directrix fo the parabola.
4. Find an equation of the conic satisfying the given conditions.
Hyperbola, foci (5, 6) and (5, –4), asymptotes x = 2y + and x = – 2y +
5. Find an equation of the conic satisfying the given conditions.
Hyperbola, foci (5, 6) and (5, –2), asymptotes x = 2y + and x = – 2y +
3
7
1
9