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9.5 Notes – Hyperbolas

9.5 Notes – Hyperbolas. ( x , y ). d 2. focus. focus. d 2 – d 1 = constant. Hyperbolas: the set of all points for which the difference of the distances to two foci is a constant. d 1. transverse. center.

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9.5 Notes – Hyperbolas

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  1. 9.5 Notes – Hyperbolas

  2. (x, y) d2 focus focus d2 – d1= constant Hyperbolas: the set of all points for which the difference of the distances to two foci is a constant. d1 transverse center The imaginary line between the focal points is the ‘transverse’ axis of the hyperbola.

  3. vertex (c, 0) focus focus c a Horizontal transverse axis asymptote

  4. focus asymptote (c, 0) c vertex a Vertical transverse axis

  5. A hyperbola can be graphed by locating the vertices (using the a distance from the center) and drawing the two asymptotes through the center of the hyperbola. The foci can be located by using the formula: .

  6. Standard Form of equation for a hyperbola (note the a2 is always in the lead term) b a b a

  7. Ex 1: State if the hyperbola is horizontal/vertical, find the center, and the eqn of asymptotes. a) horizontal (0, 0) Center:

  8. Ex 1: State if the hyperbola is horizontal/vertical, find the center, and the eqn of asymptotes. b) vertical (-2, 1) Center:

  9. Ex 2: Graph each hyperbola by filling in the missing information a) Horizontal or Vertical center: ( , ) transverse axis(eq): vertices: ( , ) ( , ) c = ______ foci: ( , ) ( , ) Asymp: 0 0 y = 0 2 0 -2 0

  10. Ex 2: Graph each hyperbola by filling in the missing information a) Horizontal or Vertical center: ( , ) transverse axis(eq): vertices: ( , ) ( , ) c = ______ foci: ( , ) ( , ) Asymp: 0 0 y = 0 2 0 -2 0 5.4 -5.4 0 5.4 0

  11. Ex 2: Graph each hyperbola by filling in the missing information a) Horizontal or Vertical center: ( , ) transverse axis(eq): vertices: ( , ) ( , ) c = ______ foci: ( , ) ( , ) Asymp: 0 0 y = 0 2 0 -2 0 5.4 5.4 0 -5.4 0

  12. Ex 2: Graph each hyperbola by filling in the missing information 36 36 36

  13. Ex 2: Graph each hyperbola by filling in the missing information Horizontal or Vertical center: ( , ) transverse axis(eq): vertices: ( , ) ( , ) c = ______ foci: ( , ) ( , ) Asymp: -2 2 x = -2 -2 8 -2 -4

  14. Ex 2: Graph each hyperbola by filling in the missing information Horizontal or Vertical center: ( , ) transverse axis(eq): vertices: ( , ) ( , ) c = ______ foci: ( , ) ( , ) Asymp: -2 2 x = -2 -2 8 -2 -4 6.1 -2 8.1 -2 -4.1

  15. Ex 2: Graph each hyperbola by filling in the missing information Horizontal or Vertical center: ( , ) transverse axis(eq): vertices: ( , ) ( , ) c = ______ foci: ( , ) ( , ) Asymp: -2 2 x = -2 -2 8 -2 -4 6.1 -2 8.1 -2 -4.1

  16. Ex 3: Write the equation of the hyperbola centered at the origin with foci (-4, 0) (4, 0) and vertices (-3, 0) and (3, 0)

  17. Ex 4: Write the equation of the hyperbola centered at the origin with foci (0, 2) (0, -2) and vertices (0, 1) and (0, -1)

  18. Ex 5: Write the eqn of the hyperbola with center (-2, 1), vertices at (-2, 5) and (-2, -3) and a b-value of 8. (-2, 5) (-2, 1) (-2, -3)

  19. Ex 6: Write the equation in standard form: 9 81 16 –16

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