Slide 7 - 1 Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc.

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Slide Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc. All rights reserved. Chapter 7 Analytic Geometry

Slide Copyright © 2009 Pearson Education, Inc. Find the equation of the parabola with focus at (3, 0) and vertex at (0, 0). a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the equation of the parabola with focus at (3, 0) and vertex at (0, 0). a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the vertex, focus, and directrix of b. c.d. a. V: (3, 1) F: (2.75, 1) D: x = 3.25 V: (–1, –3) F: (–1.25, –3) D: x = 2.75 V: (3, 1) F: (3, 0.75) D: y = 1.25 V: (–3, –1) F: (–3, –1.25) D: y = –0.75

Slide Copyright © 2009 Pearson Education, Inc. Find the vertex, focus, and directrix of b. c.d. a. V: (3, 1) F: (2.75, 1) D: x = 3.25 V: (–1, –3) F: (–1.25, –3) D: x = 2.75 V: (3, 1) F: (3, 0.75) D: y = 1.25 V: (–3, –1) F: (–3, –1.25) D: y = –0.75

Slide Copyright © 2009 Pearson Education, Inc. A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 24 inches across at its opening and is 2 feet deep, where will the light be concentrated? a.18 in. from the vertex b.1.5 in. from the vertex c.0.2 in. from the vertex d.0.1 in. from the vertex

Slide Copyright © 2009 Pearson Education, Inc. A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 24 inches across at its opening and is 2 feet deep, where will the light be concentrated? a.18 in. from the vertex b.1.5 in. from the vertex c.0.2 in. from the vertex d.0.1 in. from the vertex

Slide Copyright © 2009 Pearson Education, Inc. Find an equation for the ellipse with center at (0, 0), focus at (2, 0) and vertex at (6, 0). a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Find an equation for the ellipse with center at (0, 0), focus at (2, 0) and vertex at (6, 0). a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the center, foci, and vertices of the ellipse a.C: (–3, 1) V: (–9, 1), (3, 1) b.C: (1, –3) V: (–9, 1), (3, 1) c.C: (–3, 1) V: (6, 1), (–6, 1) d.C: (–3, 1) V: (6, 1), (–6, 1)

Slide Copyright © 2009 Pearson Education, Inc. Find the center, foci, and vertices of the ellipse a.C: (–3, 1) V: (–9, 1), (3, 1) b.C: (1, –3) V: (–9, 1), (3, 1) c.C: (–3, 1) V: (6, 1), (–6, 1) d.C: (–3, 1) V: (6, 1), (–6, 1)

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. A bridge is built in the shape of a semielliptical arch. It has a span of 110 feet. The height of the arch 29 feet from the center is to be 6 feet. Find the height of the arch at its center. a.6.22 ft b.7.06 ft c ft d ft

Slide Copyright © 2009 Pearson Education, Inc. A bridge is built in the shape of a semielliptical arch. It has a span of 110 feet. The height of the arch 29 feet from the center is to be 6 feet. Find the height of the arch at its center. a.6.22 ft b.7.06 ft c ft d ft

Slide Copyright © 2009 Pearson Education, Inc. Find an equation for the hyperbola with vertices at (0, ±10) and asymptote the line a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Find an equation for the hyperbola with vertices at (0, ±10) and asymptote the line a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the asymptotes of the hyperbola a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the asymptotes of the hyperbola a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find an equation for the hyperbola with center at (7, 8), focus at (3, 8), and vertex at (6, 8). a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Find an equation for the hyperbola with center at (7, 8), focus at (3, 8), and vertex at (6, 8). a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Two recording devices are set 3000 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 300 feet from point B, s small amount of explosive is detonated. The recording devices record the time the second reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation? a ft b ft c ftd. 675 ft

Slide Copyright © 2009 Pearson Education, Inc. Two recording devices are set 3000 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 300 feet from point B, s small amount of explosive is detonated. The recording devices record the time the second reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation? a ft b ft c ftd. 675 ft

Slide Copyright © 2009 Pearson Education, Inc. Identify the equation a.parabola b.ellipse c.hyperbola d.not a conic

Slide Copyright © 2009 Pearson Education, Inc. Identify the equation a.parabola b.ellipse c.hyperbola d.not a conic

Slide Copyright © 2009 Pearson Education, Inc. Determine the rotation formulas to use so that the new equation contains no xy-term. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Determine the rotation formulas to use so that the new equation contains no xy-term. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Rotate the axes so that the new equation contains no xy-term. Give the angle of rotation. a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Rotate the axes so that the new equation contains no xy-term. Give the angle of rotation. a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Identify the equation a.parabola b.ellipse c.hyperbola d.not a conic

Slide Copyright © 2009 Pearson Education, Inc. Identify the equation a.parabola b.ellipse c.hyperbola d.not a conic

Slide Copyright © 2009 Pearson Education, Inc. Identify the conic that the polar equation represents and give the position of the directrix. a.hyperbola; directrix perpendicular to the polar axis 3 left of the pole b.hyperbola; directrix perpendicular to the polar axis 3 right of the pole c.ellipse; directrix perpendicular to the polar axis 3 left of the pole d.ellipse; directrix perpendicular to the polar axis 3 right of the pole

Slide Copyright © 2009 Pearson Education, Inc. Identify the conic that the polar equation represents and give the position of the directrix. a.hyperbola; directrix perpendicular to the polar axis 3 left of the pole b.hyperbola; directrix perpendicular to the polar axis 3 right of the pole c.ellipse; directrix perpendicular to the polar axis 3 left of the pole d.ellipse; directrix perpendicular to the polar axis 3 right of the pole

Slide Copyright © 2009 Pearson Education, Inc. Convert a. b. c. d. to a rectangular equation.

Slide Copyright © 2009 Pearson Education, Inc. Convert a. b. c. d. to a rectangular equation.

Slide Copyright © 2009 Pearson Education, Inc. Graph the curve whose parametric equations are x = 2t – 1, y = t 2 + 2; –4 ≤ t ≤ 4. a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Graph the curve whose parametric equations are x = 2t – 1, y = t 2 + 2; –4 ≤ t ≤ 4. a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Use a graphing utility to graph the curve whose parametric equations are a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Use a graphing utility to graph the curve whose parametric equations are a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Find a rectangular equation for the plane curve defined by x = 9 sin t, y = 9 cos t; 0 ≤ t ≤ 2π. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find a rectangular equation for the plane curve defined by x = 9 sin t, y = 9 cos t; 0 ≤ t ≤ 2π. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. A baseball player hit a baseball with an initial speed of 190 feet per second at an angle of 40º to the horizontal. The ball was a hit at a height of 5 feet off the ground. Find the parametric equations that describe the motion of the ball as a function of time. a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. A baseball player hit a baseball with an initial speed of 190 feet per second at an angle of 40º to the horizontal. The ball was a hit at a height of 5 feet off the ground. Find the parametric equations that describe the motion of the ball as a function of time. a. c. b. d.

Slide Copyright © 2009 Pearson Education, Inc. Find parametric equations for y = 9x + 5. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find parametric equations for y = 9x + 5. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find parametric equations for 0 ≤ t ≤ 2 that define the curve. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find parametric equations for 0 ≤ t ≤ 2 that define the curve. a. b. c. d.