Conic Sections Project
By: Andrew Pistana
1st Hour
Honors Algebra 2
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.
Conic Sections
Click on this site for a
fun, interactive
applet!!
http://cs.jsu.edu/mcis/faculty/leath
rum/Mathlets/awl/conicsmain.html
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/
ConicSections_dir/conicSections.html
Different Forms Of Conic Sections
• Click on one of these buttons to learn
more about that form of Conic Section.
Parabolas
Ellipses
THE
END
Circles
Hyperbolas
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)
Parabolas
Parabola Links
•http://en.wikipedia.org/wiki/Derivati
ons_of_conic_sections
•http://etc.usf.edu/clipart/galleries/m
ath/conic_parabolas.php
•http://analyzemath.com/parabola/Fi
ndEqParabola.html
Click here to go
back to different
forms of Conic
Sections!
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)
Co-Vertices: (0,+/-b)
(0,+/-a)
(+/-b,0)
When finding the foci, use the following
equation….
c2 = a2 – b2
Ellipses
Ellipses
•Video:
http://www.bing.com/videos/search?q=conic+sections+ellipse&view=detail&
mid=05D6AFE5CF2D689E455F05D6AFE5CF2D689E455F&first=0&FORM
=LKVR19
Ellipses
• Useful Links:
• http://mathforum.org/library/drmath/view/6
2576.html
• http://en.wikipedia.org/wiki/Ellipse
• http://mathworld.wolfram.com/Ellipse.html
Back to different
forms of Conic
Sections
Circles
• Definition: A circle is the set of all points that
are the same distance, r, from a fixed point.
General Formula: X2 + Y2=r2 where r is the
radius
• Unlike parabolas, circles ALWAYS have X2 and
Y 2 terms.
– X2 + Y2=4 is a circle with a radius of 2 ( since 4 =22)
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
Circles
Circles
• http://www.mathwarehouse.com/geometry/
circle/equation-of-a-circle.php
• http://en.wikipedia.org/wiki/Circle
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.
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:
Hyperbolas
• http://www.youtube.com/watch?v=Z6cwpsDC_5A
Hyperbolas
• http://www.analyzemath.com/EquationHyp
erbola/EquationHyperbola.html
• http://www.slu.edu/classes/maymk/GeoGe
bra/EllipseHyperbola.html
• http://en.wikipedia.org/wiki/Hyperbola
THE END
• Thank You for looking through my
presentation!