Alg2 lesson 8-5
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The document discusses key concepts and properties of hyperbolas including asymptotes, vertices, foci, transverse axis, conjugate axis, and equations. It provides examples of writing equations of hyperbolas given values for a, b, and c and calculating vertices, foci, center, and asymptotes. The examples illustrate finding components of hyperbolas using the standard equation form.
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Alg2 lesson 8-5
- 1. HyperbolaasymptotesVertices and foci lie on the Transverse axisConjugate axisTransverse axisfocusfocusvertex
- 2. transverse axisConjugate axisTransverse axisconjugate axis
- 4. ba2 + b2 = c2ac
- 5. Write an equation for the hyperbola.Transverse axisa = 2c = 4acExample 5-1a
- 6. Write an equation for the hyperbola.Transverse axisa = 3c = 4cac2 = a2 + b242 = 32 + b216 = 9 + b27 = b2Example 5-1b
- 7. Vertices: (2, 0) and (-2, 0)Foci:Asymptotes 4 1a2b2Center: (0, 0)a = 2b = 1c2 = a2 + b2c2 = 4 + 1c = √ 5baExample 5-3a
- 8. 1 1Example 5-4a
- 9. Center: (-3, 5)a = 1Vertices: (-2, 5) and (-4, 5)b = 1c2 = a2 + b2c2 = 12 + 12c2 = 2c = 1 1Asymptotes: y = x + 8 y = -x + 2 Foci:Example 5-4a