1 / 9

10.5 Hyperbolas

10.5 Hyperbolas. p.615. Hyperbolas. Like an ellipse but instead of the sum of distances it is the difference A hyperbola is the set of all points P such that the differences from P to two fixed points, called foci, is constant

hedda-farrell
Download Presentation

10.5 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. 10.5 Hyperbolas p.615

  2. Hyperbolas • Like an ellipse but instead of the sum of distances it is the difference • A hyperbola is the set of all points P such that the differences from P to two fixed points, called foci, is constant • The line thru the foci intersects the hyperbola @ two points (the vertices) • The line segment joining the vertices is the transverse axis, and it’s midpoint is the center of the hyperbola. • Has 2 branches and 2 asymptotes • The asymptotes contain the diagonals of a rectangle centered at the hyperbolas center

  3. Asymptotes (0,b) Vertex (a,0) Vertex (-a,0) Focus Focus (0,-b) This is an example of a horizontal transverse axis (a, the biggest number, is under the x2 term with the minus before the y)

  4. Vertical transverse axis

  5. Standard Form of Hyperbola w/ center @ origin Foci lie on transverse axis, c units from the center c2 = a2+b2

  6. Graph 4x2 – 9y2 = 36 • Write in standard form (divide through by 36) • a=3 b=2 – because x2 term is ‘+’ transverse axis is horizontal & vertices are (-3,0) & (3,0) • Draw a rectangle centered at the origin. • Draw asymptotes. • Draw hyperbola.

  7. Write the equation of a hyperbole with foci (0,-3) & (0,3) and vertices (0,-2) & (0,2). • Vertical because foci & vertices lie on the y-axis • Center @ origin because f & v are equidistant from the origin • Since c=3 & a=2, c2 = b2 + a2 • 9 = b2 + 4 • 5 = b2 • +/-√5 = b

  8. Assignment

More Related