1. Translating Conic Sections

2. 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)

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 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.

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