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

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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.
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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
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