1 / 13

HYPERBOLA

HYPERBOLA. PARTS OF A HYPERBOLA. The dashed lines are asymptotes for the graphs. conjugate axis. vertices. vertices. transverse axis. center. Focus 1. Focus 2.

waite
Download Presentation

HYPERBOLA

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. HYPERBOLA

  2. PARTS OF A HYPERBOLA The dashed lines are asymptotes for the graphs conjugate axis vertices vertices transverse axis center Focus 1 Focus 2

  3. A hyperbola is the collection of points in the plane whose difference of distances from two fixed points, called the foci, is a constant. P (x,y) |dPF1 – dPF2|= 2a

  4. Curves open sideways: Horizontal Transverse axis • The x-axiscontains: • 2 vertices, (-a, 0)and (a, 0) • 2 foci at (-c, 0), (c, 0) • has length = 2a • * the conjugate axis (y-axis) has length = 2b F(c, 0) F(-c, 0) For every point P on the hyperbola we have |dPF1 – dPF2|= 2a

  5. Curves open up/down:VerticalTransverse axis. • The y-axiscontains: • 2 vertices, (0, -b) and (0, b) • 2 foci at (0, -c), (0, c) • has length = 2b • * the conjugate axis (x-axis) has length = 2a F(0, c) (0, b) (0, -b) F(0, -c) For every point P on the hyperbola we have |dPF1 – dPF2|= 2b

  6. HYPERBOLA with any center:

  7. PythagoreanProperty

  8. GraphingHyperbolas Step 1: Make a rectangle measuring 2a by 2band draw the diagonals. These are the asymptotes. Step 2: Plot the vertices on the transverse axis and draw the arches of the hyperbola b c a a b

  9. Example 1 Graph the hyperbola 4x2 – 16y2 = 64,and find the focal distance. 4x2 – 16y2 = 6464 64 64 That means a = 4and b = 2 c2=a2+b2 c2=16+4 c2 = 20 c= ±√20 Focal distance is 2√20 (0, 2) (–4,0) (4, 0) (0,-2)

  10. Example 2: Write an equation of the hyperbola centered at (0,0) whose foci are (0, –6) and (0, 6) and whose vertices are (0, –4) and (0, 4). b= 4andc = 6 c2=a2+b2 62 =a2+42 36 = 16 + a2 20 = a2 (0, 6) (0, 4) (0, –4) (0, –6)

  11. Example 3: Determine the inequality of the shaded hyperbolic region with vertex (0,12) and focus (0,15). b= 12 and c = 15 c2=a2+b2 225=a2 +144 81 = a2

  12. Example 4: Determine the inequality of the hyperbola representing the shaded region. Slope of asymptote is y = bx a Slope of asymptote:-4-0 = 4 -3-0 3 so b = 4 a 3 b = 4 6 3 b = 8

  13. Example 5: Determine the intersection point(s), if any, of the line 2x – y + 1 = 0 and the hyperbola

More Related