1014 CHAPTER 10 Analytic Geometry 61. Design of a Lithotripter A lithotripter is based on the ellipse with equation x2 36 + y2 9 = 1. How far from the center of the ellipse must the kidney stone and the source of the beam be placed? Give the exact answer. 62. Design of a Lithotripter Rework Exercise 61 if the equation of the ellipse is 9x2 + 4y2 = 36. Equations and Graphs of Hyperbolas An ellipse was defined as the set of all points in a plane the sum of whose distances from two fixed points is a constant. A hyperbola is defined similarly. 10.3 Hyperbolas ■ Equations and Graphs of Hyperbolas ■ Translated Hyperbolas ■ Eccentricity Hyperbola A hyperbola is the set of all points in a plane such that the absolute value of the difference of the distances from two fixed points is constant. The two fixed points are the foci of the hyperbola. Chapter 10 Quiz (Sections 10.1–10.2) 1. Concept Check Match each equation of a conic section in Column I with the appropriate description in Column II. I (a) x + 3 = 41y - 122 (b) 1x + 322 + 1 y - 122 = 81 (c) 251x - 222 + 1 y - 122 = 100 (d) 1x - 222 16 + 1y - 122 9 = 1 (e) -21x + 322 + 1 = y II A. circle; center 1-3, 12 B. parabola; opens right C. ellipse; major axis horizontal D. parabola; opens down E. ellipse; major axis vertical Write an equation for each conic section. 2. parabola with vertex 1-1, 22 and focus 12, 22 3. parabola with vertex at the origin; through the point A 210, -5B; opens down 4. ellipse with center 13, -22; a = 5; c = 3; major axis vertical 5. ellipse with foci at 1-3, 32 and 1-3, 112; major axis of length 10 Identify and then graph each conic section. If it is a parabola, give the vertex, focus, directrix, and axis of symmetry. If it is an ellipse, give the center, vertices, and foci. 6. y + 4 = 1x + 322 7. 4x2 + 9y2 = 36 8. 81x + 12 = 1y + 322 9. 1x + 322 25 + 1y + 222 36 = 1 10. x = -4y2 - 4y - 3
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