Algebra II Section 8-5 Hyperbolas. Hyperbola The set of all points in a plane such that the absolute value of the difference of the distances from 2 fixed.

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Presentation transcript:

Algebra II Section 8-5 Hyperbolas

Hyperbola The set of all points in a plane such that the absolute value of the difference of the distances from 2 fixed points is constant.

Center = (h, k) Transverse Axis = 2a Conjugate Axis = 2b F 1 (h-c, k) F 2 (h+c, k) a b c Vertex

What is the difference of the distances to the Foci? Also : a 2 + b 2 = c 2 a a

Standard Form “a” is always the distance from the center to the vertex.

Find the length of each axis and the coordinates of the foci and the equations of the asymptotes. b = 8 Center = (4, -5) c 2 = a 2 + b 2 c 2 = Conjugate Axis = 16 c 2 = 100 c = 10 Foci = (-6, -5) and (14, -5)

For a given diameter and height of a tower and a given strength, this shape requires less material than any other form. Hyperbolic Paraboloid

Reflection Property

Homework Page 445 #1-31 odd