1. Accel Precalc Unit 2: Algebra Topics Lesson 4: Hyperbolas (part 1)
EQ: How do you write the equation of a hyperbola and how do you use the equation to graph?

2. CONIC SECTIONS:
Hyperbola
Ellipse

3. Patty Paper Activity:
On a piece of wax paper, patty paper, or transparent paper, construct a circle using a compass or circular shaped object.
1. Label the center of your circle A.
2. Create another point OUTSIDE the circle. Label this point B.
3. Fold the paper so that point B is anywhere on the edge of the circle.  Make a crease in the paper.
4. Open the paper and place point B on another point on the edge of the circle.  Make another crease in the paper.
5.   Continue this process many times around the circle.  

5. Examples of Hyperbolas in the Real World:

7. Definition of a Hyperbola

8. ***NOTE: The transverse axis CAN be shorter than the conjugate axis.
A hyperbola has 2 axes of symmetry. One axis is called the transverse axis and its endpoints are the vertices. The other axis is called the conjugate axis and its endpoints are the co-vertices.
The two axes intersect at the center of the hyperbola.
***NOTE: The transverse axis CAN be shorter than the conjugate axis.

9. Day 23 Agenda:
DG minutes

10. A Translated Hyperbola
Standard Equation of
A Translated Hyperbola
Center
Transverse Axis
Conjugate Axis
Vertex
Co-Vertex
Foci
Asymptotes
(h, k)
Horizontal 2a
Vertical 2b
(h  a, k)
(h, k  b)
In each case: a2 + b2 = c2
(h  c, k)
Asymptotes are LINEAR! Recall: y = mx + b
d1 and d2 are the respective y-intercepts

11. A Translated Hyperbola
Standard Equation of
A Translated Hyperbola
Center
Transverse Axis
Conjugate Axis
Vertex
Co-Vertex
Foci
Asymptotes
(h, k)
Vertical 2a
Horizontal 2b
(h, k a)
(h b, k)
In each case: a2 + b2 = c2
(h, k  c)
Asymptotes are LINEAR! Recall: y = mx + b
d1 and d2 are the respective y-intercepts

12. Plot the vertices and co-vertices then draw a rectangle determined by these points. Sketch the diagonals of this rectangle (the asymptotes).

15. Assignment: textbook p. 720
#1 – 4, 6, 9, 11, 13, 23, 25, 30, 32