Section 10 6 Translating Conic Sections Translating an

Section 10. 6 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) (-3, 0) (-3, -2) (0, -4)

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) (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, a = (6 – 0))/2 ½ the distance =3 between the vertices (-1, 1) (0, 1) (6, 1) (3, 1) c = (7 – (-1))/2 =4 (7, 1) 2. Find the center, add a to lesser vertex 3. Find the length of c, ½ the distance between the two foci 4. Find the length of b, by Pythagorean theorem.

Translating a Hyperbola Relationships between: 1. Demonstrate how the location of the center of the hyperbola moves. 2. 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 (-1, 1) (0, 1) (6, 1) (3, 1) c = (7 – (-1))/2 =4 (7, 1) 1. 2. 3. 4. a= 3 Center: (3, 1) c=4 42 = 32 + b 2 16 = 9 + b 2 7 = b 2

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

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