Translating Conic Sections

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Presentation transcript:

Translating Conic Sections

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

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)

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 to lesser 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.

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

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

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)

Assignment