1. Today in Precalculus Go over homework Notes: Hyperbolas
Completing the square
Eccentricity
Homework

2. Hyperbolas
Prove that the graph of 9x2 – 4y2 – 18x + 8y + 41 = 0 is an hyperbola. Find the center, vertices and foci. Then graph the hyperbola by hand.
9x2 – 18x – 4y2 + 8y = -41
9(x2 – 2x) – 4(y2 – 2y) = -41
9(x2 – 2x + 1) – 4(y2 – 2y + 1) =
9(x – 1)2 – 4(y – 1)2 = -36

3. Center: (1, 1)
a = ±3
Vertices: (1, -2), (1, 4)
c2 = 9 +4 = 13
c = ±3.6
Foci: (1, -2.6), (1,4.6 )
Pts on conjugate axis
b = ±2
(-1,1), (3,1)

4. Example 2
Prove that the graph of 9y2 – 25x2 + 72y – 100x +269 = 0 is an hyperbola. Find the center, vertices and foci. Then graph the hyperbola by hand.
9y2 + 72y – 25x2 – 100x = -269
9(y2 + 8y) – 25(x2 + 4x) = - 269
9(y2 + 8y + 16) – 25(x2 + 4x + 4) =
9(y + 4)2 – 25(x + 2)2 = -225

5. Center: (-2, -4)
a = ± 3
Vertices: (-5, -4), (1, -4)
c2 = =34
c = ±5.8
Foci: (-7.8, -4), (3.8, -4)
Pts on conjugate axis
b = ±5
(-2, -9), (-2, 1)

6. Eccentricity Where a is the semitranvserse axis and
b is the semiconjugate axis.
Example a:
Example b:

7. Homework
Page 664: 47-50
Ellipse and Hyperbola Quiz: Tuesday, February 26