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2 Thank you for purchasing this product! Please stop back at my store and let me know how it went. Follow me to learn of new products, sales, and freebies. Website: Pinterest: Joan Kessler Products by Joan Kessler (distancemath.com) may be used by the purchaser for their classroom use only. All rights reserved. No part of this publication may be electronically reproduced, distributed, or transmitted without the written permission of the author. This includes posting this product on the internet in any form, including classroom/personal websites or network drives. Your license is for one user. You cannot alter the file, and redistribute it as your own, nor any derivatives of it. You may use this as many times as you like for YOUR classes. If you want to share, direct your colleagues to my store to purchase or buy multiple licenses at a discount. School licenses available.
3 Product Description This resource is designed for PreCalculus or Geometry. Included: There are two sets of 12 illustrated task cards related to applications of conics, one set has QR codes with the answers and one set does not. Hyperbolas, Ellipses, and parabolas are included in the real world applications. *Master List of questions which can be used for an alternate class or for an absentee. *Two quizzes or additional HW assignments with similar problems. *Answer key *Student response sheet with room for work and unnumbered so you can choose the cards you want.
4 Ideas for Task Cards First, print the cards on card stock. These print out well in black and white but can be decorated with a highlighter before laminating. Laminating makes the cards more durable and they can be used year after year. Print a copies of the student response sheet for each student. There are multiple ways to use these task cards in your classroom. Students can work alone, randomly pair up, or work in small groups. When students work in pairs or small groups, give as many task cards as there are students. This way they can help each other, work together, and each student has a task. After a few minutes, depending upon the difficulty level and your experience, each group passes their cards to the next group. You may also set up math stations with these cards. If you are new to task cards please download a free product which describes and explains Task Cards. It is full of great ideas written by a great teacher. Here is a shortened link to it. me if there are any questions.
5 1. The roof of a building is in the shape of the hyperbola, y 2 x 2 =15 where x and y are in meters. Refer to the figure and determine the height, h, of the outside walls. 2. A nuclear cooling tower cross section is a hyperbola having a diameter of 60 ft. at the center. The distance between the two foci is 98 ft. What is the equation for the hyperbola? 3. A comet follows the hyperbolic path 2 2 described by x y - =1 2 4 where x and y are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path? 4. A carpenter wants to cut the largest possible ellipse from a 11 ft by 12 ft rectangular board. After the foci are located, a string is connected to them and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.
6 5. A rectangular board is 16 ft. by 20 ft. How far from the center of the board should the foci be located in order to cut the largest elliptical tabletop from the board? 6. A field microphone used at a soccer game has a parabolic cross section and is 20 in. wide at the opening. The focus is 9 in. from the vertex. Find the depth of the microphone. 7. A cross-section of an irrigation canal is a parabola. If the surface of the water is 40 ft. wide and the canal is 28 ft. deep at the center, how deep is it 18 ft. from the edge? 40 ft. 8. A satellite dish has a parabolic cross section and is 6 ft. deep. The focus is 16 ft. from the vertex. Find the width of the satellite dish at the opening. Round your answer to the nearest foot.
7 9. A building has an entry with the shape of a parabolic arch 8 ft. high and 34 ft. wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. 10. A railroad tunnel is shaped like a semiellipse. The height of the tunnel at the center is 28 ft. and the vertical clearance must be 14 ft. at a point 18 ft. from the center. Find an equation for the ellipse. 11. An elliptical riding path is to be built on a rectangular piece of property that measures 6 mi. by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides. 12. A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.
8 1. The roof of a building is in the shape of the hyperbola, y 2 x 2 =15 where x and y are in meters. Refer to the figure and determine the height, h, of the outside walls. 2. A nuclear cooling tower cross section is a hyperbola having a diameter of 60 ft. at the center. The distance between the two foci is 98 ft. What is the equation for the hyperbola? 3. A comet follows the hyperbolic path 2 2 described by x y - =1 2 4 where x and y are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path? 4. A carpenter wants to cut the largest possible ellipse from a 11 ft by 12 ft rectangular board. After the foci are located, a string is connected to them and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.
9 5. A rectangular board is 16 ft. by 20 ft. How far from the center of the board should the foci be located in order to cut the largest elliptical tabletop from the board? 6. A field microphone used at a soccer game has a parabolic cross section and is 20 in. wide at the opening. The focus is 9 in. from the vertex. Find the depth of the microphone. 7. A cross-section of an irrigation canal is a parabola. If the surface of the water is 40 ft. wide and the canal is 28 ft. deep at the center, how deep is it 18 ft. from the edge? 40 ft. 8. A satellite dish has a parabolic cross section and is 6 ft. deep. The focus is 16 ft. from the vertex. Find the width of the satellite dish at the opening. Round your answer to the nearest foot.
10 9. A building has an entry with the shape of a parabolic arch 8 ft. high and 34 ft. wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. 10. A railroad tunnel is shaped like a semiellipse. The height of the tunnel at the center is 28 ft. and the vertical clearance must be 14 ft. at a point 18 ft. from the center. Find an equation for the ellipse. 11. An elliptical riding path is to be built on a rectangular piece of property that measures 6 mi. by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides. 12. A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.
11
12 Applications to Conics Name Class Date Solve. 1) The roof of a building is in the shape of the hyperbola y 2 - x 2 = 15, where x and y are in meters. Refer to the figure and determine the height h of the outside walls. A = 9 m 2) A nuclear cooling tower cross section is a hyperbola having a diameter of 60 ft at the center. The distance between the two foci is 98 ft. What is the equation for the hyperbola? 3) A comet follows the hyperbolic path described by x2 2 - y2 4 = 1, where x and y are in millions of miles. If the sun is the focus of the path, how close to the sun is the vertex of the path? 4) A carpenter wants to cut the largest possible ellipse from a 11 ft by 12 ft rectangular board. After the foci are located, a string is connected to them and pulled taut by a pencil in order to draw the ellipse. Find the length of the string. (c) 2015 joan s kessler distancemath.com 1
13 5) A rectangular board is 16 ft by 20 ft. How far from the center of the board should the foci be located in order to cut the largest elliptical tabletop from the board? 6) A field microphone used at a soccer game has a parabolic cross section and is 20 in. wide at the opening. The focus is 9 in. from the vertex. Find the depth of the microphone. 7) A cross-section of an irrigation canal is a parabola. If the surface of the water is 40 ft wide and the canal is 28 ft deep at the center, how deep is it 18 ft from the edge? 8) A satellite dish has a parabolic cross section and is 6 ft deep. The focus is 16 ft from the vertex. Find the width of the satellite dish at the opening. Round your answer to the nearest foot. 9) A building has an entry with the shape of a parabolic arch 8 ft high and 34 ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. A = 8 ft B = 34 ft 10) A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 28 ft and the vertical clearance must be 14 ft at a point 18 ft from the center. Find an equation for the ellipse. (c) 2015 joan s kessler distancemath.com 2
14 11) An elliptical riding path is to be built on a rectangular piece of property that measures 6 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides. A = 6 mi B = 4 mi Solve the problem. 12) A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places. (c) 2015 joan s kessler distancemath.com 3
15 Applications to Conics Name Class Date Solve. 1) A flashlight used at inma mine has a parabolic cross section and is 30 in. wide at the opening. The focus is 9 in. from the vertex. Find the depth of the microphone. 2) The roof of a building is in the shape of the hyperbola y 2 - x 2 = 20, where x and y are in meters. Refer to the figure and determine the height h of the outside walls. A = 9 m (c) 2015 joan s kessler distancemath.com A-1
16 3) The path of a dolphin jumping is shaped like a semi-ellipse. The maximum height above the water at the center is 44 ft. Its height is 22 ft at a point 9 ft from the center. Find an equation for the elliptical path. 4) A satellite dish has a parabolic cross section and is 8 ft deep. The focus is 16 ft from the vertex. Find the width of the satellite dish at the opening. Round your answer to the nearest foot. 5) A nuclear cooling tower cross section is a hyperbola having a diameter of 50 ft at the center. The distance between the two foci is 100 ft. What is the equation for the hyperbola? (c) 2015 joan s kessler distancemath.com A-2
17 Answer Key Testname: CONICS APPLICATIONS QUIZ 1) 6.25 in. 2) 10 m x 2 3) y = 1 4) 45 ft x 2 5) y = 1 (c) 2015 joan s kessler distancemath.com A-3
18 Applications to Conics Name Class Date Solve. 1) The path of a dolphin jumping is shaped like a semi-ellipse. The maximum height above the water at the center is 48 ft. Its height is 16 ft at a point 8 ft from the center. Find an equation for the elliptical path. (c) 2015 joan s kessler distancemath.com B-1
19 2) The roof of a building is in the shape of the hyperbola y 2 - x 2 = 15, where x and y are in meters. Refer to the figure and determine the height h of the outside walls. A = 9 m 3) A flashlight used at inma mine has a parabolic cross section and is 22 in. wide at the opening. The focus is 25 in. from the vertex. Find the depth of the microphone. (c) 2015 joan s kessler distancemath.com B-2
20 4) A nuclear cooling tower cross section is a hyperbola having a diameter of 62 ft at the center. The distance between the two foci is 98 ft. What is the equation for the hyperbola? 5) A satellite dish has a parabolic cross section and is 10 ft deep. The focus is 16 ft from the vertex. Find the width of the satellite dish at the opening. Round your answer to the nearest foot. (c) 2015 joan s kessler distancemath.com B-3
21 Answer Key Testname: CONICS APPLICATIONS QUIZ 1) x y = 1 2) 9.8 m 3) 1.21 in. x 2 4) y = 1 5) 51 ft (c) 2015 joan s kessler distancemath.com B-4
22 Applications to Conics Name Class Date
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