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hyperbole

marghe.zilli

Created on April 2, 2024

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Transcript

Hyperbola

Margherita e Giovanni

The Tour Eiffel can be an example of hyperbola

in fact...

Definition and equation

Assigned in the Cartesian plane two points, F1 and F2, is called hyperbola the geometric place of the points P of the plane that have constant the difference, in absolute value, of the distances from F1 and F2

x2 y2 --- - --- = 1 a2 b2

F:(±c;0)

V:(±a; 0)

C=√a2+b2

e: c/a

b y: - --- ⋅x a

b y: --- ⋅x a

If the hyperbola is vertical...

  • V:(0;±a)
  • F:(0;±c)
  • y: a/b ⋅x
  • y: a/b ⋅x
  • e: c/b

x2 y2 --- - --- = -1 a2 b2

Exercise

Given the equation of the hyperbola find the vertices, foci, asymptotes and eccentricity; then draw them

x2 y2 - ---- = 4 4

home exercises: pg 444 ex 10 and 19

Fine!