Answer: The orbits of stars, planets, comets, asteroids, and satellites all have the
Chapter 10, Problem 68(choose chapter or problem)
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 = 1What do you notice about the values of e for the equationsyou identified as hyperbolas?
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