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Easy Conics 0 Student Tasks for Mastery

Easy Conics 0 Student Tasks for Mastery. For testing, Math 140 students should be able to: Identify a graph image of simple shapes by name Read image’s symmetry, constants ( h , k, a, b, c, r ) and location of special points: center ( h , k ), vertices, foci

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Easy Conics 0 Student Tasks for Mastery

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  1. Easy Conics 0Student Tasks for Mastery For testing, Math 140 students should be able to: Identify a graph image of simple shapes by name Read image’s symmetry, constants (h, k, a, b, c, r) and location of special points: center (h, k), vertices, foci Write equation of simple conic shapes Read an equation identifying a simple shape’s name, symmetry, image constants (h, k, a, b, c, r), & coordinates of points: center (h, k), vertices, & foci Put equations into standard form by completing squares so preceding can be read

  2. Hyperbola Easy Conics 1Shapes Circle Ellipse Note: Overall shapes may be translated or rotated. Parabola

  3. Hyperbola Easy Conics 2Centers Circle Ellipse Note: Overall shapes may be translated or rotated. Parabola

  4. Hyperbola Easy Conics 3Vertices (singular: vertex) Circle none Ellipse Note: Overall shapes may be translated or rotated. Parabola

  5. Hyperbola Easy Conics 4Foci (singular: focus) Circle Ellipse Note: Overall shapes may be translated or rotated. Parabola

  6. Hyperbola Easy Conics 5Axes: Major (Transverse) & Minor Circle Ellipse Note: Overall shapes may be translated or rotated. Parabola

  7. Easy Conics 6Equations & Constants: Circle y Circle (x –h)2 + (y –k)2 = r2 _______ (x –h)2 + (y –k)2 = 1 ___r2r2 Ellipse & hyperbola have similar equations to this. r Position of center if curve is translated: (h, k). Recall equation for circle: x (h,k)

  8. 2c Ellipse Easy Conics 7Equations & Constants: Ellipse y Ellipse (x –h)2 + (y –k)2 = 1 a2b2 Case shown in figure is a > b. Otherwise major axis is vertical and we switch letters. Let c > 0 and c2 = a2 - b2. Figure has foci at (h +c, k). a b Position of center if curve is translated: (h, k). The equation for ellipse is: x (h,k)

  9. c a 2c Hyperbola (h,k) Easy Conics 8Equations & Constants: Hyperbola y (x –h)2 - (y –k)2 = +1 a2b2 Case shown in figure is minus. Otherwise major axis is horizontal. Shown is b > a. Let c > 0 and ______c2 = a2 + b2.Figure has foci at (h, k +c). b a Position of center if curve is translated: (h, k). The equation for hyperbola is: x (h,k)

  10. a Easy Conics 9Equations & Constants: Parabola Parabola y y –k = (x –h)2 _ ____ 4a If major axis is horizontal, interchange x y and h k. Figure has focus at (h, k + a). Position of center if curve is translated: (h, k). The equation for parabola is: x (h,k) Note: (y –k) is not squared, one focus, no b & c.

  11. Easy Conics 10Student Tasks for Mastery For testing, Math 140 students should be able to: Identify a graph image of simple shapes by name Read image’s symmetry, constants (h, k, a, b, c, r) and location of special points: center (h, k), vertices, foci Write equation of simple conic shapes Read an equation identifying a simple shape’s name, symmetry, image constants (h, k, a, b, c, r), & coordinates of points: center (h, k), vertices, & foci Put equations into standard form by completing squares so preceding can be read

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