Deck 9: Extension E: Vectors and the Geometry of Space

Question 1

Write a polar equation in r and $\theta$ of an ellipse with the focus at the origin,with the eccentricity and directrix

A)
B)
C)
D)
E)

Answer 1

Question 2

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)

Answer 2

Question 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)

Answer 3

Question 4

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.

Question 5

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

Question 6

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.

Question 7

Write a polar equation of the conic that has a focus at the origin,eccentricity ,and directrix Identify the conic.

A) , ellipse
B) , hyperbola
C) , hyperbola
D) , ellipse

Question 8

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

Question 9

Find the eccentricity of the conic.

A)
B)
C)
D)
E)