Homework Help is Here – Start Your Trial Now!
Math
Calculus
The reflective property of parabolas The accompanying fig- ure shows a typical point P(xo, yo) on the parabola y² = 4px. The line L is tangent to the parabola at P. The parabola's focus lies at F(p, 0). The ray L' extending from P to the right is parallel to the x-axis. We show that light from F to P will be reflected out along L' by showing that B equals a. Establish this equality by taking the following steps. a. Show that tan ß = 2p/yo- b. Show that tan þ Yo/(xo – p). c. Use the identity tan o – tan ß tan a 1 + tan ø tan ß to show that tan a = 2p/yo- Since a and ß are both acute, tan ß = tan a implies ß = a. This reflective property of parabolas is used in applications like car headlights, radio telescopes, and satellite TV dishes. y Р(Хо. Уo) L' |Уo F(p, 0) y² = 4px

The reflective property of parabolas The accompanying fig- ure shows a typical point P(xo, yo) on the parabola y² = 4px. The line L is tangent to the parabola at P. The parabola's focus lies at F(p, 0). The ray L' extending from P to the right is parallel to the x-axis. We show that light from F to P will be reflected out along L' by showing that B equals a. Establish this equality by taking the following steps. a. Show that tan ß = 2p/yo- b. Show that tan þ Yo/(xo – p). c. Use the identity tan o – tan ß tan a 1 + tan ø tan ß to show that tan a = 2p/yo- Since a and ß are both acute, tan ß = tan a implies ß = a. This reflective property of parabolas is used in applications like car headlights, radio telescopes, and satellite TV dishes. y Р(Хо. Уo) L' |Уo F(p, 0) y² = 4px

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 65E
See similar textbooks
icon
Related questions
Question
The reflective property of parabolas The accompanying fig- ure shows a typical point P(xo, yo) on the parabola y² = 4px. The line L is tangent to the parabola at P. The parabola's focus lies at F(p, 0). The ray L' extending from P to the right is parallel to the x-axis. We show that light from F to P will be reflected out along L' by showing that B equals a. Establish this equality by taking the following steps. a. Show that tan ß = 2p/yo- b. Show that tan þ Yo/(xo – p). c. Use the identity tan o – tan ß tan a 1 + tan ø tan ß to show that tan a = 2p/yo- Since a and ß are both acute, tan ß = tan a implies ß = a. This reflective property of parabolas is used in applications like car headlights, radio telescopes, and satellite TV dishes. y Р(Хо. Уo) L' |Уo F(p, 0) y² = 4px
Transcribed Image Text:The reflective property of parabolas The accompanying fig- ure shows a typical point P(xo, yo) on the parabola y² = 4px. The line L is tangent to the parabola at P. The parabola's focus lies at F(p, 0). The ray L' extending from P to the right is parallel to the x-axis. We show that light from F to P will be reflected out along L' by showing that B equals a. Establish this equality by taking the following steps. a. Show that tan ß = 2p/yo- b. Show that tan þ Yo/(xo – p). c. Use the identity tan o – tan ß tan a 1 + tan ø tan ß to show that tan a = 2p/yo- Since a and ß are both acute, tan ß = tan a implies ß = a. This reflective property of parabolas is used in applications like car headlights, radio telescopes, and satellite TV dishes. y Р(Хо. Уo) L' |Уo F(p, 0) y² = 4px
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS