1 / 7

10.4 Hyperbolas

10.4 Hyperbolas. JMerrill 2010. Definition. A hyperbola is the set of all points in a plane, the difference of whose distances from two distinct fixed point (foci) is a positive constant. Equations of Hyperbolas. Writing the Equation.

reid
Download Presentation

10.4 Hyperbolas

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. 10.4Hyperbolas JMerrill 2010

  2. Definition A hyperbola is the set of all points in a plane, the difference of whose distances from two distinct fixed point (foci) is a positive constant.

  3. Equations of Hyperbolas

  4. Writing the Equation • Find the equation of the hyperbola with vertices(-3, 2), (3, 2) and foci (-5, 2), (5, 2). Graph.  

  5. Find and Graph the Hyperbola • State the direction of the transverse axis, sketch a graph and find the center, the vertices, and the foci. • transverse axis: • vertical • center: • (-2, 1) • vertices: • (-2, 3), (-2, -1) • foci:

  6. Writing the Equation in Standard Form – You Try • Given 4x2 – 3y2 + 8x + 16 = 0 • You must complete the square

  7. Eccentricity • The same formula applies to both ellipses and hyperbolas. • If the eccentricity is large, the branches of the hyperbola are nearly flat. • If the eccentricity is close to 1, the branches are more narrow.

More Related