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Translating Ellipses and Hyperbolas

This assignment covers the translation of ellipses and hyperbolas, including finding equations, lengths of axes and distances between vertices and foci.

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Translating Ellipses and Hyperbolas

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  1. Translating Conic Sections Section 10.6

  2. Translating an Ellipse (0, 4) (-3, 0) (3, 0) (0, -4) Write an equation of an ellipse with center (-3, -2), vertical major axis of length 8 and minor axis of length 6. (-3, -2)

  3. Translating an Ellipse Write an equation of an ellipse with center (1, 8), horizontal major axis of length 16 and minor axis of length 10. (1, 8) (0, 5) (-8, 0) (8, 0) (0, -5)

  4. Translating a Hyperbola Write an equation of a hyperbola with vertices (0, 1) and (6, 1) and foci (-1, 1) and (7, 1) 1. Find the length of a, ½ the distance between the vertices a = (6 – 0))/2 = 3 2. Find the center, add a tolesser vertex (7, 1) (-1, 1) (0, 1) (6, 1) (3, 1) 3. Find the length of c, ½ the distance between the two foci c = (7 – (-1))/2 = 4 4. Find the length of b, by Pythagorean theorem.

  5. Translating a Hyperbola • Relationships between: • Demonstrate how the location of the center of the hyperbola moves. • Finding the length of c • Horizontal_Hyperbola.html • Vertical_Hyperbola.html

  6. Translating a Hyperbola Write an equation of a hyperbola with vertices (0, 1) and (6, 1) and foci (-1, 1) and (7, 1) a = (6 – 0))/2 = 3 • a= 3 • Center: (3, 1) • c = 4 • 42 = 32 + b2 • 16 = 9 + b2 • 7 = b2 (7, 1) (-1, 1) (0, 1) (6, 1) (3, 1) c = (7 – (-1))/2 = 4

  7. Translating a Hyperbola Write an equation of a hyperbola with vertices (2, -1) and (2, 7) and foci (2, 10) and (2, -4) • b= 4 • Center: (2, 3) • c = 7 • 72 = a2 + 42 • 49 = a2 + 16 • 33 = a2 (2, 10) (2, 7) b = (7 +1))/2 = 4 c = (10 + 4)/2 = 7 (2, 3) (2, -1) (2, -4)

  8. Assignment

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