1. Write a polar equation in r and {image} of a parabola with the focus at the origin and directrix x = 2. 1.
{image} 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Write a polar equation in r and {image} of a hyperbola with the focus at the origin, with the eccentricity 2 and the directrix x = - 9. 1. 2.
{image} 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Find the eccentricity of the conic. {image}1. 2.
{image} 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Classify the conic. {image}
parabola
hyperbola
ellipse
circle 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. The orbit of Halley?s comet, last seen in 1986 and due to return in 2062, is an ellipse with eccentricity 0.98 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 a(1 - e) and the aphelion distance is a(1 + e) .) Find the answer in AU and round to the nearest hundredth.
39.27 AU
35.83 AU
35.10 AU 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

6. The distance from the planet Mercury to the Sun is {image} km at perihelion and {image} km at aphelion. If the perihelion distance from a planet to the Sun is a(1 - e) and the aphelion distance is a(1 + e), find the eccentricity of Mercury's orbit. Round your answer to three decimal places.
e=0.214
e=0.074
e=0.258
e=0.173 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50