Solution: The orbits of stars, planets, comets, asteroids, and satellites all have the

Chapter 10, Problem 69

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The orbits of stars, planets, comets, asteroids, and satellites all have the shape of one of the conic sections. Astronomers use a measure called eccentricity to describe the shape and elongation of an orbital path. For the circle and ellipse, eccentricity e is calculated with the formula e = c d , where c 2 = 0 a2 - b2 0 and d is the larger value of a or b. For a hyperbola, eccentricity e is calculated with the formula e = c d , where c 2 = a2 + b2 and the value of d is equal to a if the hyperbola has x-intercepts or equal to b if the hyperbola has y-intercepts. Use equations AH to answer Exercises 6170.A. x2 36 - y2 13 = 1 B. x2 4 + y2 4 = 1 C. x2 25 + y2 16 = 1 D. y2 25 - x2 39 = 1 E. x2 17 + y2 81 = 1 F. x2 36 + y2 36 = 1 G. x2 16 - y2 65 = 1 H. x2 144 + y2 140 = 1The eccentricity of a parabola is exactly 1. Use this informationand the observations you made in Exercises 66, 67,and 68 to describe a way that could be used to identify thetype of conic section based on its eccentricity value.