1. Conic Sections Project
By: Andrew Pistana
1st Hour
Honors Algebra 2

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.

3. Conic Sections Click on this site for a fun, interactive applet!!

4. Conic Sections Learn more about Conic Sections on these websites!

5. 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

6. 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)

7. Parabolas

8. Parabola Links
Click here to go back to different forms of Conic Sections!

9. 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

10. Ellipses

11. Ellipses
Video:

12. Ellipses Useful Links:
Back to different forms of Conic Sections

13. 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)

14. 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

15. Circles

16. Circles

17. 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.

18. 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:

19. Hyperbolas

20. Hyperbolas

21. THE END
Thank You for looking through my presentation!