Accel Precalc Unit 2: Algebra Topics Lesson 4: Hyperbolas (part 1)

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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?

CONIC SECTIONS: Hyperbola Ellipse

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.

Examples of Hyperbolas in the Real World:

Definition of a Hyperbola

***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.

Day 23 Agenda: DG12 --- 15 minutes

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

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

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

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