Find the focus and directrix of the parabola . Example 2: Find the focus and the directrix of the parabola x' = 4y.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 39RE
icon
Related questions
icon
Concept explainers
Topic Video
Question
Help solving
ll Boost Mobile
9:52 AM
Unit 6 - Parabolas w Vertex at O...
Parabolas with Vertex at Origin
vertex: lies halfway between the
focus and the directrix.
focus: lies on the axis of
symmetry
directrix: is perpendicular to the
axis of symmetry
focus
%23
vertex
directrix
Characteristics of Parabolas with vertex (0, 0)
Standard Equation x = 4py y = 4px
Up/down Left/right
(0, р)
Орens
Focus
(р. 0)
Directrix
y = -p x= -p
Axis of Symmetry y-axis
X-ахis
To calculate these values, you will need to follow the following
directions:
1) Get the squared term by itself. (IF necessary!)
2) Set the number next to either x/y equal to 4p, then solve for
4p.
3) Substitute the value of p into the formulas from the table.
Example 1: Finding the Focus and Directrix
Find the focus and directrix of the parabola.
Example 2:
Find the focus and the directrix of the parabola x² = 4y.
8.
9.
000
Dashboard
Calendar
To Do
Notifications
Inbox
Transcribed Image Text:ll Boost Mobile 9:52 AM Unit 6 - Parabolas w Vertex at O... Parabolas with Vertex at Origin vertex: lies halfway between the focus and the directrix. focus: lies on the axis of symmetry directrix: is perpendicular to the axis of symmetry focus %23 vertex directrix Characteristics of Parabolas with vertex (0, 0) Standard Equation x = 4py y = 4px Up/down Left/right (0, р) Орens Focus (р. 0) Directrix y = -p x= -p Axis of Symmetry y-axis X-ахis To calculate these values, you will need to follow the following directions: 1) Get the squared term by itself. (IF necessary!) 2) Set the number next to either x/y equal to 4p, then solve for 4p. 3) Substitute the value of p into the formulas from the table. Example 1: Finding the Focus and Directrix Find the focus and directrix of the parabola. Example 2: Find the focus and the directrix of the parabola x² = 4y. 8. 9. 000 Dashboard Calendar To Do Notifications Inbox
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning