Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 9.3, Problem 35WE
To determine

To prove: The length of the latus rectum is twice the distance from the focus to the directrix.

Expert Solution & Answer
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Explanation of Solution

Given information: The perpendicular line passes through the focus and intersects the parabola at two points.

Proof: Let D be the directrix line and f be the focus point.

Hence,

  FD=PDFQ=PQ

As the line PQ is perpendicular to the axis: PQ=PF+FQ

  PQ=PF+FQPQ=FD+FDPQ=2FD

The latus rectum of a parabola is the chord that passes through its focus. It is perpendicular to the major axis of a parabola. Its length is equal to the four times the focal length or just two times the distance from the focus to the directrix line.

Chapter 9 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 9.1 - Prob. 11OECh. 9.1 - Prob. 12OECh. 9.1 - Prob. 13OECh. 9.1 - Prob. 14OECh. 9.1 - Prob. 15OECh. 9.1 - Prob. 1WECh. 9.1 - Prob. 2WECh. 9.1 - Prob. 3WECh. 9.1 - Prob. 4WECh. 9.1 - Prob. 5WECh. 9.1 - Prob. 6WECh. 9.1 - Prob. 7WECh. 9.1 - Prob. 8WECh. 9.1 - Prob. 9WECh. 9.1 - Prob. 10WECh. 9.1 - Prob. 11WECh. 9.1 - Prob. 12WECh. 9.1 - Prob. 13WECh. 9.1 - Prob. 14WECh. 9.1 - Prob. 15WECh. 9.1 - Prob. 16WECh. 9.1 - Prob. 17WECh. 9.1 - Prob. 18WECh. 9.1 - Prob. 19WECh. 9.1 - Prob. 20WECh. 9.1 - Prob. 21WECh. 9.1 - Prob. 22WECh. 9.1 - Prob. 23WECh. 9.1 - Prob. 24WECh. 9.1 - Prob. 25WECh. 9.1 - Prob. 26WECh. 9.1 - Prob. 27WECh. 9.1 - Prob. 28WECh. 9.1 - Prob. 29WECh. 9.1 - Prob. 30WECh. 9.1 - Prob. 31WECh. 9.1 - Prob. 32WECh. 9.1 - Prob. 1PCh. 9.1 - Prob. 2PCh. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Prob. 5PCh. 9.1 - Prob. 6PCh. 9.1 - Prob. 7PCh. 9.1 - Prob. 8PCh. 9.1 - Prob. 9PCh. 9.1 - Prob. 10PCh. 9.1 - Prob. 11PCh. 9.1 - Prob. 12PCh. 9.1 - Prob. 13PCh. 9.1 - Prob. 14PCh. 9.1 - Prob. 1MRECh. 9.1 - Prob. 2MRECh. 9.1 - Prob. 3MRECh. 9.1 - Prob. 4MRECh. 9.1 - Prob. 5MRECh. 9.1 - Prob. 6MRECh. 9.1 - Prob. 1CECh. 9.1 - Prob. 2CECh. 9.1 - Prob. 3CECh. 9.1 - Prob. 4CECh. 9.2 - Prob. 1OECh. 9.2 - Prob. 2OECh. 9.2 - Prob. 3OECh. 9.2 - Prob. 4OECh. 9.2 - Prob. 5OECh. 9.2 - Prob. 6OECh. 9.2 - Prob. 7OECh. 9.2 - Prob. 8OECh. 9.2 - Prob. 9OECh. 9.2 - Prob. 10OECh. 9.2 - Prob. 11OECh. 9.2 - Prob. 12OECh. 9.2 - Prob. 13OECh. 9.2 - Prob. 14OECh. 9.2 - Prob. 15OECh. 9.2 - Prob. 1WECh. 9.2 - Prob. 2WECh. 9.2 - Prob. 3WECh. 9.2 - Prob. 4WECh. 9.2 - Prob. 5WECh. 9.2 - Prob. 6WECh. 9.2 - Prob. 7WECh. 9.2 - Prob. 8WECh. 9.2 - Prob. 9WECh. 9.2 - Prob. 10WECh. 9.2 - Prob. 11WECh. 9.2 - Prob. 12WECh. 9.2 - Prob. 13WECh. 9.2 - Prob. 14WECh. 9.2 - Prob. 15WECh. 9.2 - Prob. 16WECh. 9.2 - Prob. 17WECh. 9.2 - Prob. 18WECh. 9.2 - Prob. 19WECh. 9.2 - Prob. 20WECh. 9.2 - Prob. 21WECh. 9.2 - Prob. 22WECh. 9.2 - Prob. 23WECh. 9.2 - Prob. 24WECh. 9.2 - Prob. 25WECh. 9.2 - Prob. 26WECh. 9.2 - Prob. 27WECh. 9.2 - Prob. 28WECh. 9.2 - Prob. 29WECh. 9.2 - Prob. 30WECh. 9.2 - Prob. 31WECh. 9.2 - Prob. 32WECh. 9.2 - Prob. 33WECh. 9.2 - Prob. 34WECh. 9.2 - Prob. 35WECh. 9.2 - Prob. 36WECh. 9.2 - Prob. 37WECh. 9.2 - Prob. 38WECh. 9.2 - Prob. 39WECh. 9.2 - Prob. 40WECh. 9.2 - Prob. 41WECh. 9.2 - Prob. 42WECh. 9.2 - Prob. 43WECh. 9.2 - Prob. 44WECh. 9.2 - Prob. 45WECh. 9.2 - Prob. 46WECh. 9.2 - Prob. 47WECh. 9.2 - Prob. 48WECh. 9.2 - Prob. 49WECh. 9.2 - Prob. 50WECh. 9.3 - Prob. 1OECh. 9.3 - Prob. 2OECh. 9.3 - Prob. 3OECh. 9.3 - Prob. 4OECh. 9.3 - Prob. 5OECh. 9.3 - Prob. 6OECh. 9.3 - Prob. 7OECh. 9.3 - Prob. 8OECh. 9.3 - Prob. 9OECh. 9.3 - Prob. 10OECh. 9.3 - Prob. 11OECh. 9.3 - Prob. 12OECh. 9.3 - Prob. 1WECh. 9.3 - Prob. 2WECh. 9.3 - Prob. 3WECh. 9.3 - Prob. 4WECh. 9.3 - Prob. 5WECh. 9.3 - Prob. 6WECh. 9.3 - Prob. 7WECh. 9.3 - Prob. 8WECh. 9.3 - Prob. 9WECh. 9.3 - Prob. 10WECh. 9.3 - Prob. 11WECh. 9.3 - Prob. 12WECh. 9.3 - Prob. 13WECh. 9.3 - Prob. 14WECh. 9.3 - Prob. 15WECh. 9.3 - Prob. 16WECh. 9.3 - Prob. 17WECh. 9.3 - Prob. 18WECh. 9.3 - Prob. 19WECh. 9.3 - Prob. 20WECh. 9.3 - Prob. 21WECh. 9.3 - Prob. 22WECh. 9.3 - Prob. 23WECh. 9.3 - Prob. 24WECh. 9.3 - Prob. 25WECh. 9.3 - Prob. 26WECh. 9.3 - Prob. 27WECh. 9.3 - Prob. 28WECh. 9.3 - Prob. 29WECh. 9.3 - Prob. 30WECh. 9.3 - Prob. 31WECh. 9.3 - Prob. 32WECh. 9.3 - Prob. 33WECh. 9.3 - Prob. 34WECh. 9.3 - Prob. 35WECh. 9.3 - Prob. 36WECh. 9.3 - Prob. 37WECh. 9.3 - Prob. 38WECh. 9.3 - Prob. 1MRECh. 9.3 - Prob. 2MRECh. 9.3 - Prob. 3MRECh. 9.3 - Prob. 4MRECh. 9.3 - Prob. 5MRECh. 9.3 - Prob. 6MRECh. 9.3 - Prob. 1STCh. 9.3 - Prob. 2STCh. 9.3 - Prob. 3STCh. 9.3 - Prob. 4STCh. 9.3 - Prob. 5STCh. 9.3 - Prob. 6STCh. 9.3 - Prob. 7STCh. 9.3 - Prob. 8STCh. 9.4 - Prob. 1OECh. 9.4 - Prob. 2OECh. 9.4 - Prob. 3OECh. 9.4 - Prob. 4OECh. 9.4 - Prob. 5OECh. 9.4 - Prob. 6OECh. 9.4 - Prob. 1WECh. 9.4 - Prob. 2WECh. 9.4 - Prob. 3WECh. 9.4 - Prob. 4WECh. 9.4 - Prob. 5WECh. 9.4 - Prob. 6WECh. 9.4 - Prob. 7WECh. 9.4 - Prob. 8WECh. 9.4 - Prob. 9WECh. 9.4 - Prob. 10WECh. 9.4 - Prob. 11WECh. 9.4 - Prob. 12WECh. 9.4 - Prob. 13WECh. 9.4 - Prob. 14WECh. 9.4 - Prob. 15WECh. 9.4 - Prob. 16WECh. 9.4 - Prob. 17WECh. 9.4 - Prob. 18WECh. 9.4 - Prob. 19WECh. 9.4 - Prob. 20WECh. 9.4 - Prob. 21WECh. 9.4 - Prob. 22WECh. 9.4 - Prob. 23WECh. 9.4 - Prob. 24WECh. 9.4 - Prob. 25WECh. 9.4 - Prob. 26WECh. 9.4 - Prob. 27WECh. 9.4 - Prob. 28WECh. 9.4 - Prob. 29WECh. 9.4 - Prob. 30WECh. 9.4 - Prob. 31WECh. 9.4 - Prob. 32WECh. 9.4 - Prob. 33WECh. 9.4 - Prob. 34WECh. 9.4 - Prob. 35WECh. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.5 - Prob. 1OECh. 9.5 - Prob. 2OECh. 9.5 - Prob. 3OECh. 9.5 - Prob. 4OECh. 9.5 - Prob. 5OECh. 9.5 - Prob. 6OECh. 9.5 - Prob. 7OECh. 9.5 - Prob. 8OECh. 9.5 - Prob. 9OECh. 9.5 - Prob. 1WECh. 9.5 - Prob. 2WECh. 9.5 - Prob. 3WECh. 9.5 - Prob. 4WECh. 9.5 - Prob. 5WECh. 9.5 - Prob. 6WECh. 9.5 - Prob. 7WECh. 9.5 - Prob. 8WECh. 9.5 - Prob. 9WECh. 9.5 - Prob. 10WECh. 9.5 - Prob. 11WECh. 9.5 - Prob. 12WECh. 9.5 - Prob. 13WECh. 9.5 - Prob. 14WECh. 9.5 - Prob. 15WECh. 9.5 - Prob. 16WECh. 9.5 - Prob. 17WECh. 9.5 - Prob. 18WECh. 9.5 - Prob. 19WECh. 9.5 - Prob. 20WECh. 9.5 - Prob. 21WECh. 9.5 - Prob. 22WECh. 9.5 - Prob. 23WECh. 9.5 - Prob. 24WECh. 9.5 - Prob. 25WECh. 9.5 - Prob. 26WECh. 9.5 - Prob. 27WECh. 9.5 - Prob. 28WECh. 9.5 - Prob. 29WECh. 9.5 - Prob. 30WECh. 9.5 - Prob. 31WECh. 9.5 - Prob. 32WECh. 9.5 - Prob. 33WECh. 9.5 - Prob. 34WECh. 9.5 - Prob. 35WECh. 9.5 - Prob. 1MRECh. 9.5 - Prob. 2MRECh. 9.5 - Prob. 3MRECh. 9.5 - Prob. 4MRECh. 9.5 - Prob. 5MRECh. 9.5 - Prob. 6MRECh. 9.5 - Prob. 7MRECh. 9.5 - Prob. 8MRECh. 9.5 - Prob. 9MRECh. 9.5 - Prob. 10MRECh. 9.6 - Prob. 1OECh. 9.6 - Prob. 2OECh. 9.6 - Prob. 3OECh. 9.6 - Prob. 4OECh. 9.6 - Prob. 5OECh. 9.6 - Prob. 6OECh. 9.6 - Prob. 7OECh. 9.6 - Prob. 8OECh. 9.6 - Prob. 9OECh. 9.6 - Prob. 10OECh. 9.6 - Prob. 11OECh. 9.6 - Prob. 12OECh. 9.6 - Prob. 13OECh. 9.6 - Prob. 14OECh. 9.6 - Prob. 1WECh. 9.6 - Prob. 2WECh. 9.6 - Prob. 3WECh. 9.6 - Prob. 4WECh. 9.6 - Prob. 5WECh. 9.6 - Prob. 6WECh. 9.6 - Prob. 7WECh. 9.6 - Prob. 8WECh. 9.6 - Prob. 9WECh. 9.6 - Prob. 10WECh. 9.6 - Prob. 11WECh. 9.6 - Prob. 12WECh. 9.6 - Prob. 13WECh. 9.6 - Prob. 14WECh. 9.6 - Prob. 15WECh. 9.6 - Prob. 16WECh. 9.6 - Prob. 17WECh. 9.6 - Prob. 18WECh. 9.6 - Prob. 19WECh. 9.6 - Prob. 20WECh. 9.6 - Prob. 21WECh. 9.6 - Prob. 1STCh. 9.6 - Prob. 2STCh. 9.6 - Prob. 3STCh. 9.6 - Prob. 4STCh. 9.6 - Prob. 5STCh. 9.6 - Prob. 6STCh. 9.7 - Prob. 1OECh. 9.7 - Prob. 2OECh. 9.7 - Prob. 3OECh. 9.7 - Prob. 4OECh. 9.7 - Prob. 5OECh. 9.7 - Prob. 6OECh. 9.7 - Prob. 7OECh. 9.7 - Prob. 8OECh. 9.7 - Prob. 9OECh. 9.7 - Prob. 10OECh. 9.7 - Prob. 11OECh. 9.7 - Prob. 12OECh. 9.7 - Prob. 1WECh. 9.7 - Prob. 2WECh. 9.7 - Prob. 3WECh. 9.7 - Prob. 4WECh. 9.7 - Prob. 5WECh. 9.7 - Prob. 6WECh. 9.7 - Prob. 7WECh. 9.7 - Prob. 8WECh. 9.7 - Prob. 9WECh. 9.7 - Prob. 10WECh. 9.7 - Prob. 11WECh. 9.7 - Prob. 12WECh. 9.7 - Prob. 13WECh. 9.7 - Prob. 14WECh. 9.7 - Prob. 15WECh. 9.7 - Prob. 16WECh. 9.7 - Prob. 17WECh. 9.7 - Prob. 18WECh. 9.7 - Prob. 19WECh. 9.7 - Prob. 20WECh. 9.7 - Prob. 1MRECh. 9.7 - Prob. 2MRECh. 9.7 - Prob. 3MRECh. 9.7 - Prob. 4MRECh. 9.7 - Prob. 5MRECh. 9.7 - Prob. 6MRECh. 9.7 - Prob. 7MRECh. 9.8 - Prob. 1OECh. 9.8 - Prob. 2OECh. 9.8 - Prob. 3OECh. 9.8 - Prob. 1WECh. 9.8 - Prob. 2WECh. 9.8 - Prob. 3WECh. 9.8 - Prob. 4WECh. 9.8 - Prob. 5WECh. 9.8 - Prob. 6WECh. 9.8 - Prob. 7WECh. 9.8 - Prob. 8WECh. 9.8 - Prob. 9WECh. 9.8 - Prob. 10WECh. 9.8 - Prob. 11WECh. 9.8 - Prob. 12WECh. 9.8 - Prob. 13WECh. 9.8 - Prob. 14WECh. 9.8 - Prob. 15WECh. 9.8 - Prob. 16WECh. 9.8 - Prob. 17WECh. 9.8 - Prob. 18WECh. 9.8 - Prob. 19WECh. 9.8 - Prob. 20WECh. 9.8 - Prob. 21WECh. 9.8 - Prob. 22WECh. 9.8 - Prob. 23WECh. 9.8 - Prob. 24WECh. 9.8 - Prob. 25WECh. 9.8 - Prob. 26WECh. 9.8 - Prob. 1PCh. 9.8 - Prob. 2PCh. 9.8 - Prob. 3PCh. 9.8 - Prob. 4PCh. 9.8 - Prob. 5PCh. 9.8 - Prob. 6PCh. 9.8 - Prob. 7PCh. 9.8 - Prob. 8PCh. 9.8 - Prob. 9PCh. 9.8 - Prob. 10PCh. 9.8 - Prob. 11PCh. 9.8 - Prob. 12PCh. 9.8 - Prob. 13PCh. 9.8 - Prob. 14PCh. 9.9 - Prob. 1OECh. 9.9 - Prob. 2OECh. 9.9 - Prob. 3OECh. 9.9 - Prob. 4OECh. 9.9 - Prob. 5OECh. 9.9 - Prob. 6OECh. 9.9 - Prob. 7OECh. 9.9 - Prob. 8OECh. 9.9 - Prob. 9OECh. 9.9 - Prob. 10OECh. 9.9 - Prob. 11OECh. 9.9 - Prob. 12OECh. 9.9 - Prob. 1WECh. 9.9 - Prob. 2WECh. 9.9 - Prob. 3WECh. 9.9 - Prob. 4WECh. 9.9 - Prob. 5WECh. 9.9 - Prob. 6WECh. 9.9 - Prob. 7WECh. 9.9 - Prob. 8WECh. 9.9 - Prob. 9WECh. 9.9 - Prob. 10WECh. 9.9 - Prob. 11WECh. 9.9 - Prob. 12WECh. 9.9 - Prob. 13WECh. 9.9 - Prob. 14WECh. 9.9 - Prob. 15WECh. 9.9 - Prob. 16WECh. 9.9 - Prob. 17WECh. 9.9 - Prob. 18WECh. 9.9 - Prob. 19WECh. 9.9 - Prob. 20WECh. 9.9 - Prob. 21WECh. 9.9 - Prob. 22WECh. 9.9 - Prob. 23WECh. 9.9 - Prob. 24WECh. 9.9 - Prob. 25WECh. 9.9 - Prob. 1PCh. 9.9 - Prob. 2PCh. 9.9 - Prob. 3PCh. 9.9 - Prob. 4PCh. 9.9 - Prob. 5PCh. 9.9 - Prob. 6PCh. 9.9 - Prob. 7PCh. 9.9 - Prob. 8PCh. 9.9 - Prob. 9PCh. 9.9 - Prob. 10PCh. 9.9 - Prob. 11PCh. 9.9 - Prob. 12PCh. 9.9 - Prob. 1MRECh. 9.9 - Prob. 2MRECh. 9.9 - Prob. 3MRECh. 9.9 - Prob. 4MRECh. 9.9 - Prob. 5MRECh. 9.9 - Prob. 6MRECh. 9.9 - Prob. 7MRECh. 9.9 - Prob. 8MRECh. 9.9 - Prob. 9MRECh. 9.9 - Prob. 10MRECh. 9.9 - Prob. 11MRECh. 9.9 - Prob. 1STCh. 9.9 - Prob. 2STCh. 9.9 - Prob. 3STCh. 9.9 - Prob. 4STCh. 9.9 - Prob. 5STCh. 9.9 - Prob. 6STCh. 9.9 - Prob. 7STCh. 9 - Prob. 1CRCh. 9 - Prob. 2CRCh. 9 - Prob. 3CRCh. 9 - Prob. 4CRCh. 9 - Prob. 5CRCh. 9 - Prob. 6CRCh. 9 - Prob. 7CRCh. 9 - Prob. 8CRCh. 9 - Prob. 9CRCh. 9 - Prob. 10CRCh. 9 - Prob. 11CRCh. 9 - Prob. 12CRCh. 9 - Prob. 13CRCh. 9 - Prob. 14CRCh. 9 - Prob. 15CRCh. 9 - Prob. 16CRCh. 9 - Prob. 17CRCh. 9 - Prob. 18CRCh. 9 - Prob. 19CRCh. 9 - Prob. 20CRCh. 9 - Prob. 1CTCh. 9 - Prob. 2CTCh. 9 - Prob. 3CTCh. 9 - Prob. 4CTCh. 9 - Prob. 5CTCh. 9 - Prob. 6CTCh. 9 - Prob. 7CTCh. 9 - Prob. 8CTCh. 9 - Prob. 9CTCh. 9 - Prob. 10CTCh. 9 - Prob. 11CTCh. 9 - Prob. 12CTCh. 9 - Prob. 13CTCh. 9 - Prob. 14CTCh. 9 - Prob. 15CT

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