Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at...

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Notes Over 10.2 Graphing an Equation of a Parabola Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) py x 4 2 p , 0 focus y x 12 2 3 , 0 p y directr ix 3 y

Transcript of Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at...

Page 1: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

Notes Over 10.2Graphing an Equation of a ParabolaGraphing an Equation of a ParabolaStandard Equation of a Parabola (Vertex at Origin)

pyx 42

p ,0focus

yx 122

3 ,0py

directrix3y

Page 2: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

Notes Over 10.2Graphing an Equation of a ParabolaGraphing an Equation of a ParabolaStandard Equation of a Parabola (Vertex at Origin)

pxy 42

0 ,pfocus

xy 122

0 ,3px

directrix

3x

Page 3: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

Notes Over 10.2Graphing an Equation of a ParabolaGraphing an Equation of a ParabolaGraph the equation. Identify the focus and directrix of the parabola.

yx 2 .1 2

focus:

2

1 ,0

directrix:2

1y

24 p2

1p

Page 4: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

Notes Over 10.2Graphing an Equation of a ParabolaGraphing an Equation of a ParabolaGraph the equation. Identify the focus and directrix of the parabola.

xy 16 .2 2

focus: 0 ,4

directrix: 4x

164 p 4p

Page 5: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

Notes Over 10.2Graphing an Equation of a ParabolaGraphing an Equation of a ParabolaGraph the equation. Identify the focus and directrix of the parabola.

yx4

1 .3 2

focus:

16

1 ,0

directrix:16

1y

4

14 p

16

1p

Page 6: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

Notes Over 10.2Graphing an Equation of a ParabolaGraphing an Equation of a ParabolaGraph the equation. Identify the focus and directrix of the parabola.

xy 4 .4 2

focus: 0 ,1

directrix: 1x

44 p 1p

Page 7: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

1 ,0 .5

Notes Over 10.2Writing an Equation of a ParabolaWriting an Equation of a ParabolaWrite the standard form of the equation of the parabola with the given focus and vertex at (0, 0).

yx 42 pyx 42

1 yx 42

0 ,

2

1 .6

xy 42

pxy 42

2

1 xy 22

Page 8: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

4

1 ,0 .8

Notes Over 10.2Writing an Equation of a ParabolaWriting an Equation of a ParabolaWrite the standard form of the equation of the parabola with the given focus and vertex at (0, 0).

yx 42

pyx 42

4

1yx 2

0 ,2 .7

xy 42

pxy 42 2 xy 82

Page 9: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

Notes Over 10.2Modeling a Parabolic ReflectorModeling a Parabolic Reflector9. A searchlight reflector is designed so that a cross section through its axis is a parabola and the light source is at the focus. Find the focus if the reflector is 3 feet across at the opening and 1 foot deep.

1 ,5.1

ypx 42 25.1

4

25.2p

p425.2

400

22516

9

1

Page 10: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

Notes Over 10.2Modeling a Parabolic ReflectorModeling a Parabolic Reflector10. One of the largest radio telescopes has a diameter of 250 feet and a focal length of 50 feet. If the cross section of the radio telescope is a parabola, find the depth.

yx 42 pyx 42

50yx 2002

2

250

y2001252

125y200625,15

ft 1.78y

Page 11: Notes Over 10.2 Graphing an Equation of a Parabola Standard Equation of a Parabola (Vertex at Origin) focus directrix.

Notes Over 10.2


Find the equation used to graph this parabola .

Find the equation used to graph this parabola .

 · 54. E 2010 A Let M be the foot of the perpendicular from a point P on the parabola — — 3) onto its directrix and let S be the focus Of the parabola.

 · 54. E 2010 A Let M be the foot of the perpendicular from a point P on the parabola — — 3) onto its directrix and let S be the focus Of the parabola.

Parabola: from the Graph to the Equation with Innovative Formulas

Parabola: from the Graph to the Equation with Innovative Formulas

10. PARABOLAIllustration 4: Find the vertex, the axis, the focus, the directrix, and latus rectum of the parabola, 4y2 + 12x – 20y + 67 = 0. (JEE MAIN) Sol: Represent the given equation

10. PARABOLAIllustration 4: Find the vertex, the axis, the focus, the directrix, and latus rectum of the parabola, 4y2 + 12x – 20y + 67 = 0. (JEE MAIN) Sol: Represent the given equation

CCGPS Frameworks Student Edition Mathematics · WRITING THE EQUATIONS OF PARABOLAS ... 2 Derive the equation of a parabola given a focus and directrix. ... Performance Standards Framework

CCGPS Frameworks Student Edition Mathematics · WRITING THE EQUATIONS OF PARABOLAS ... 2 Derive the equation of a parabola given a focus and directrix. ... Performance Standards Framework

GOVERNMENT POLYTECHNIC, NAGPUR. in an engineering field. ... To draw parabola by i)Directrix ... any ten sketches covering all the topics under chapter 6

GOVERNMENT POLYTECHNIC, NAGPUR. in an engineering field. ... To draw parabola by i)Directrix ... any ten sketches covering all the topics under chapter 6

Parabolas. The parabola: focus directrix -A curve on which all points are equidistant from a focus and a line called the directrix. c dPF = dPdirectrix.

Parabolas. The parabola: focus directrix -A curve on which all points are equidistant from a focus and a line called the directrix. c dPF = dPdirectrix.

SZ3 DAILY PRACTICE SHEET MATHEMATICS PARABOLA …mdpcos.files.wordpress.com/2020/06/sz1-a-parabola.pdfthe parabola — 2px such that it touches the directrix of the parabola, the point

SZ3 DAILY PRACTICE SHEET MATHEMATICS PARABOLA …mdpcos.files.wordpress.com/2020/06/sz1-a-parabola.pdfthe parabola — 2px such that it touches the directrix of the parabola, the point

RadfordMathematics.com Vertex Form of the Parabola...RadfordMathematics.com Vertex Form of the Parabola Finding the Equation of a Parabola Worksheet 1 Click on the link in the header

RadfordMathematics.com Vertex Form of the Parabola...RadfordMathematics.com Vertex Form of the Parabola Finding the Equation of a Parabola Worksheet 1 Click on the link in the header

5-4 Focus and Directrix of a Parabola - … Focus and Directrix of a Parabola 170 Lesson 5-4 Focus and Directrix of a Parabola x directrix Vertical Parabola axis of symmetry y Focus

5-4 Focus and Directrix of a Parabola - … Focus and Directrix of a Parabola 170 Lesson 5-4 Focus and Directrix of a Parabola x directrix Vertical Parabola axis of symmetry y Focus

Section 9.3 The Parabola Objectives · 2015-08-16 · Section 9.3 The Parabola 903 Solution The given equation,is in the standard form so We can find both the focus and the directrix

Section 9.3 The Parabola Objectives · 2015-08-16 · Section 9.3 The Parabola 903 Solution The given equation,is in the standard form so We can find both the focus and the directrix

Chapter 10. Write an equation given the focus and directrix. Use the distance formula.

Chapter 10. Write an equation given the focus and directrix. Use the distance formula.

Lecture 7 (Hyperbola and Focus Directrix Equation)

Lecture 7 (Hyperbola and Focus Directrix Equation)

What is the standard form of a parabola who has a focus of ( 1,5) and a directrix of y=11.

What is the standard form of a parabola who has a focus of ( 1,5) and a directrix of y=11.

2.3 Focus of a Parabola - wtps.org · Section 2.3 Focus of a Parabola 69 You can derive the equation of a parabola that opens up or down with vertex (0, 0), focus (0, p), and directrix

2.3 Focus of a Parabola - wtps.org · Section 2.3 Focus of a Parabola 69 You can derive the equation of a parabola that opens up or down with vertex (0, 0), focus (0, p), and directrix

Scale - Eng Deans · 2016. 2. 26. · Parabola intuition 2 Make one parabola overlap with another by adjusting the focus coordinates and directrix. Solving quadratics by factoring

Scale - Eng Deans · 2016. 2. 26. · Parabola intuition 2 Make one parabola overlap with another by adjusting the focus coordinates and directrix. Solving quadratics by factoring

10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every.

10-5 Parabola. Parabola – “u” shape formed by quadratics. Created but all points equal distance from a focus and a given line called the directrix. Every.

circle hyperbola circle · 8/3/2016  · of the axis of symmetry with the parabola. Focus Directrix Axis of Symmetry Vertex. The definition of the parabola is the set of points the

circle hyperbola circle · 8/3/2016  · of the axis of symmetry with the parabola. Focus Directrix Axis of Symmetry Vertex. The definition of the parabola is the set of points the

0616AII Common Core State Standards · 2018-02-20 · 30 The directrix of the parabola 12(y +3) =(x −4)2 has the equation y =−6. Find the coordinates of the focus of the Find

0616AII Common Core State Standards · 2018-02-20 · 30 The directrix of the parabola 12(y +3) =(x −4)2 has the equation y =−6. Find the coordinates of the focus of the Find

8.1 Parabola comp.notebook...8.1 Parabola comp.notebook 8 April 02, 2020 Apr 12 10:13 AM Ex. 4 Prove that the graph of y2 4x + 6y +29=0 is a parabola, find its vertex, focus and directrix

8.1 Parabola comp.notebook...8.1 Parabola comp.notebook 8 April 02, 2020 Apr 12 10:13 AM Ex. 4 Prove that the graph of y2 4x + 6y +29=0 is a parabola, find its vertex, focus and directrix