Precalculus
Precalculus
9th Edition
ISBN: 9780321716835
Author: Michael Sullivan
Publisher: Addison Wesley
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Textbook Question
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Chapter 10.2, Problem 20AYU

In Problems 21-38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus at ( 0 ,  2 ) ; vertex at ( 0 ,  0 )

Expert Solution
Check Mark
To determine

(a & b)

The equation of the parabola described and two points that define the latus rectum for the following description.

Focus at ( 0, 2 ) ; vertex at ( 0, 0 ) .

Answer to Problem 20AYU

x 2  = 8y , Latus rectum: ( 4, 2 ) and ( 4, 2 ) .

Explanation of Solution

Given:

Focus at ( 0, 2 ) ; vertex at ( 0, 0 ) .

Formula used:

Vertex Focus Directrix Equation Description
( 0, 0 ) ( 0, a ) y = a x 2  = 4ay Parabola, axis of symmetry is y-axis , opens up

Calculation:

The vertex V( 0, 0 ) and focus F( 0, 2 ) both lie on the vertical line x = 0 (The axis of symmetry). The distance a from the vertex V( 0, 0 ) to the focus F( 0, 2 ) is a = 2 .

Also, because the focus F( 0, 2 ) lies above the vertex, the parabola opens up.

x 2  = 4a( y ) ; where a = 2 . Therefore the equation is,

x 2  = 4 * 2( y )

x 2  = 8y

The equation of the parabola is x 2  = 8y .

To find the points that define the latus rectum, Let us substitute y = 2 in the above equation.

x 2  = 8 * 2

x = ±4

Hence ( 4, 2 ) and ( 4, 2 ) defines the latus rectum.

Expert Solution
Check Mark
To determine

c.

To graph: The parabola for the equation x 2  = 8y .

Answer to Problem 20AYU

Precalculus, Chapter 10.2, Problem 20AYU , additional homework tip  1

Explanation of Solution

Given:

Focus at ( 0, 2 ) ; vertex at ( 0, 0 ) .

Calculation:

The graph of x 2  = 8y is plotted below.

Precalculus, Chapter 10.2, Problem 20AYU , additional homework tip  2

Using the given information V(0, 0) and F(0, 2) we have formed the equation and plotted the graph for x 2  = 8y . The focus F(0, 2) and the vertex V(0, 0) lie on the horizontal line.

The equation for directrix D: y = 2 is shown as dotted line. The parabola opens up. The points ( 4, 2 ) and ( 4, 2 ) define the latus rectum.

Chapter 10 Solutions

Precalculus

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Prob. 29RECh. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Prob. 49RECh. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - Prob. 56RECh. 10 - Prob. 57RECh. 10 - Prob. 58RECh. 10 - Prob. 59RECh. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - Prob. 65RECh. 10 - Prob. 66RECh. 10 - Prob. 67RECh. 10 - Prob. 68RECh. 10 - Prob. 69RECh. 10 - Prob. 70RECh. 10 - Prob. 71RECh. 10 - Prob. 72RECh. 10 - Prob. 73RECh. 10 - Prob. 74RECh. 10 - Prob. 75RECh. 10 - Prob. 76RECh. 10 - Prob. 77RECh. 10 - Prob. 78RECh. 10 - Prob. 79RECh. 10 - Prob. 80RECh. 10 - Prob. 81RECh. 10 - Prob. 82RECh. 10 - Prob. 83RECh. 10 - Prob. 84RECh. 10 - In Problems 13, identify each equation. If it is a...Ch. 10 - In Problems 13, identify each equation. If it is a...Ch. 10 - In Problems identify each equation. If it is a...Ch. 10 - In Problems 46, find an equation of the conic...Ch. 10 - In Problems find an equation of the conic...Ch. 10 - In Problems find an equation of the conic...Ch. 10 - In Problems 79, identify each conic without...Ch. 10 - In Problems 79, identify each conic without...Ch. 10 - In Problems identify each conic without completing...Ch. 10 - Prob. 10CTCh. 10 - Prob. 11CTCh. 10 - Prob. 12CTCh. 10 - A parabolic reflector (paraboloid of revolution)...Ch. 10 - For find Ch. 10 - In the complex number system, solve the equation ...Ch. 10 - For what numbers x is 6xx2 ?Ch. 10 - Prob. 4CRCh. 10 - Prob. 5CRCh. 10 - Prob. 6CRCh. 10 - Prob. 7CRCh. 10 - Prob. 8CRCh. 10 - Prob. 9CRCh. 10 - Prob. 10CRCh. 10 - Solve the equation where. Ch. 10 - Find the rectangle equation of the plane curve...
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Publisher:PEARSON
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ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
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ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
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Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
Finding The Focus and Directrix of a Parabola - Conic Sections; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=KYgmOTLbuqE;License: Standard YouTube License, CC-BY