1 / 22

Hyberbola

Hyberbola. Conic Sections. The plane can intersect two nappes of the cone resulting in a hyperbola . Hyperbola. Hyperbola - Definition. A hyperbola is the set of all points in a plane such that the difference in the distances from two points (foci) is constant.

emmly
Download Presentation

Hyberbola

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Hyberbola Conic Sections

  2. The plane can intersect two nappes of the cone resulting in a hyperbola. Hyperbola

  3. Hyperbola - Definition A hyperbola is the set of all points in a plane such that the difference in the distances from two points (foci) is constant. | d1 – d2 | is a constant value.

  4. Hyperbola - Definition What is the constant value for the difference in the distance from the two foci? Let the two foci be (c, 0) and (-c, 0). The vertices are (a, 0) and (-a, 0). | d1 – d2| is the constant. If the length of d2 is subtracted from the left side of d1, what is the length which remains? | d1 – d2 | = 2a

  5. Hyperbola - Equation where c2 = a2 + b2 Recognition:How do you tell a hyperbola from an ellipse? Answer:A hyperbola has a minus (-) between the terms while an ellipse has a plus (+).

  6. Graph - Example #1 Hyperbola

  7. Hyperbola - Graph Graph: Center: (-3, -2) The hyperbola opens in the “x” direction because “x” is positive. Transverse Axis: y = -2

  8. Hyperbola - Graph Graph: Vertices (2, -2) (-4, -2) Construct a rectangle by moving 4 unitsup and down from the vertices. Construct the diagonals of the rectangle.

  9. Hyperbola - Graph Graph: Draw the hyperbola touching the vertices and approaching the asymptotes. Where are the foci?

  10. Hyperbola - Graph Graph: The foci are 5 units from the center on the transverse axis. Foci: (-6, -2) (4, -2)

  11. Hyperbola - Graph Graph: Find the equation of the asymptote lines. 4 3 Use point-slope formy – y1 = m(x – x1) since the center is on both lines. -4 Slope = Asymptote Equations

  12. Graph - Example #2 Hyperbola

  13. Hyperbola - Graph Sketch the graph without a grapher: Recognition:How do you determine the type of conic section? Answer:The squared terms have opposite signs. Write the equation in hyperbolic form.

  14. Hyperbola - Graph Sketch the graph without a grapher:

  15. Hyperbola - Graph Sketch the graph without a grapher: Center: (-1, 2) Transverse Axis Direction: Up/Down Equation: x=-1 Vertices: Up/Down from the center or

  16. Hyperbola - Graph Sketch the graph without a grapher: Plot the rectangular points and draw the asymptotes. Sketch the hyperbola.

  17. Hyperbola - Graph Sketch the graph without a grapher: Plot the foci. Foci:

  18. Hyperbola - Graph Sketch the graph without a grapher: Equation of the asymptotes:

  19. Finding an Equation Hyperbola

  20. Hyperbola – Find an Equation Find the equation of a hyperbola with foci at (2, 6) and (2, -4). The transverse axis length is 6.

  21. Conic Section Recogition

  22. Recognizing a Conic Section Parabola - One squared term. Solve for the term which is not squared. Complete the square on the squared term. Ellipse - Two squared terms. Both terms are the same “sign”. Circle - Two squared terms with the same coefficient. Hyperbola - Two squared terms with opposite “signs”.

More Related