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Today in Precalculus

Today in Precalculus. Turn in page 654: 45-48,59,60 Go over homework Notes: Hyperbolas center (h,k) Homework. Hyperbolas center not (0,0).

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Today in Precalculus

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  1. Today in Precalculus • Turn in page 654: 45-48,59,60 • Go over homework • Notes: Hyperbolas center (h,k) • Homework

  2. Hyperbolas center not (0,0) When a hyperbola is translated horizontally by h units and vertically by k units, the center of the hyperbola moves from (0,0) to (h,k). Such a translation does not change the length of the transverse or conjugate axis or the Pythagorean relation. Center (h,k) foci on x=h Center (h,k) foci on y=k

  3. Hyperbola with center (h,k)

  4. Example 1 Find the vertices and foci of the hyperbola Center: (4, -2) a2 = 6 a = ±2.4 Vertices: (1.6, -2), (6.4, -2) c2 = 10 + 6 = 16 c = ±4 Foci: (0, -2), (8, -2)

  5. Example 2 Find the standard form of the equation for the hyperbola whose transverse axis has endpoints (-2, -1) and (8, -1), and whose conjugate axis has length 8. 2a = 10 a = 5 Center (3, -1) 2b = 8 b = 4

  6. Sketching a hyperbola Sketch the graph of the hyperbola by hand. Center (-2, 1) a2 = 16, a = ±4 Vertices:(-6, 1),(2,1) b2 = 5, b = ±2.2 Pts on conjugate axis (-2,-1.2), (-2,3.2) c2 = 16+5, c= ±4.6 foci:(-6.6,1),(2.6,1) Asymptotes:

  7. Graphing a hyperbola Like the other conic sections, must solve the equation for y

  8. Homework Pg 663: 3, 4, 7-10, 15, 16, 21, 22, 33-36, 51, 52

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