Conic Sections Project

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Conic Sections Project

• By Andrew Pistana
• 1st Hour
• Honors Algebra 2

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Conic Sections

• A conic section is a geometric curve formed by
  cutting a cone. A curve produced by the
  intersection of a plane with a circular cone.
  Some examples of conic sections are parabolas,
  ellipses, circles, and hyperbolas.

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Conic Sections
Click on this site for a fun, interactive
applet!! http//cs.jsu.edu/mcis/faculty/leathrum/M
athlets/awl/conics-main.html
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Conic Sections

• Learn more about Conic Sections on these
  websites!
• http//en.wikipedia.org/wiki/Conic_section
• http//math2.org/math/algebra/conics.htm
• http//xahlee.org/SpecialPlaneCurves_dir/ConicSec
  tions_dir/conicSections.html

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Different Forms Of Conic Sections

• Click on one of these buttons to learn more about
  that form of Conic Section.

Parabolas
Ellipses
THE END
Hyperbolas
Circles
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Parabolas

• A parabola is a mathematical curve, formed by the
  intersection of a cone with a plane parallel to
  its side.

Equation Focus Directrix Axis of Symmetry
x2 4py (0,p) y -p Vertical (x 0)
y2 4px (p,0) x -p Horizontal (y 0)
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Parabolas
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Parabola Links

• http//en.wikipedia.org/wiki/Derivations_of_conic_
  sections
• http//etc.usf.edu/clipart/galleries/math/conic_pa
  rabolas.php
• http//analyzemath.com/parabola/FindEqParabola.htm
  l

Click here to go back to different forms of Conic
Sections!
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Ellipses

• An ellipse is an intersection of a cone and
  oblique plane that does not intersect the base of
  the cone.
• Standard Form

Vertices (/-a,0)
(0,/-a) Co-Vertices (0,/-b)
(/-b,0)
When finding the foci, use the following
equation. c2 a2 b2
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Ellipses
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Ellipses

• Video http//www.bing.com/videos/search?qconics
  ectionsellipseviewdetailmid05D6AFE5CF2D689E45
  5F05D6AFE5CF2D689E455Ffirst0FORMLKVR19

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Ellipses

• Useful Links
• http//mathforum.org/library/drmath/view/62576.htm
  l
• http//en.wikipedia.org/wiki/Ellipse
• http//mathworld.wolfram.com/Ellipse.html

Back to different forms of Conic Sections
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Circles

• Definition A circle is the set of all points
  that are the same distance, r, from a fixed
  point.General Formula X2 Y2r2 where r is the
  radius
• Unlike parabolas, circles ALWAYS have X2 and Y 2
  terms.
• X2 Y24 is a circle with a radius of 2 ( since
  4 22)

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Circle Example Problem

• What is the equation of the circle pictured on
  the graph below?  Answer  Since the radius of
  this this circle is 1, and its center is the
  origin, this picture's equation is (Y-0)²
  (X-0)² 1 ² Y² X² 1

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Circles
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Circles

• http//www.mathwarehouse.com/geometry/circle/equat
  ion-of-a-circle.php
• http//en.wikipedia.org/wiki/Circle

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Hyperbolas

• A hyperbola is a conic section formed by a point
  that moves in a plane so that the difference in
  its distance from two fixed points in the plane
  remains constant.

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Hyperbolas

• Focus of hyperbola the two points on the
  transverse axis. These points are what controls
  the entire shape of the hyperbola since the
  hyperbola's graph is made up of all points, P,
  such that the distance between P and the two foci
  are equal. To determine the foci you can use the
  formula a2 b2 c2
• Transverse axis this is the axis on which the
  two foci are.
• Asymptotes the two lines that the hyperbolas
  come closer and closer to touching. The
  asymptotes are colored red in the graphs below
  and the equation of the asymptotes is always

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Hyperbolas

• http//www.youtube.com/watch?vZ6cwpsDC_5A

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Hyperbolas

• http//www.analyzemath.com/EquationHyperbola/Equat
  ionHyperbola.html
• http//www.slu.edu/classes/maymk/GeoGebra/EllipseH
  yperbola.html
• http//en.wikipedia.org/wiki/Hyperbola

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THE END

• Thank You for looking through my presentation!