Honors PreCalculus
Chapter 9 –
Analytic Geometry
Mrs. Carey
Chapter 9
Assignments
11/26
12/3
M:
p. 672 1-8, 31-47 o
T:
p. 672 15-29 o, 57, 59, 61
W:
p. 684 1-8, 9-15 o, 33-39 o
R:
p. 685 19-25 o, 45-61 o
F:
p. 699 1-4, 19-23 o, 39-47 o skip 43
M:
p. 700 9-17 o, 31-37 o, 53, 55
T:
Review
W:
Review
R:
Ch 9 Test
Honors Pre-Calculus
9.1- 9.2
Conics and Parabolas
Learning Targets: Students will be able to see an overview of conic sections. Students will be able to graph parabolas.
9.1 Conics
9.2 Parabolas
Vertical
y  x2
Horizontal
y   x2
x  y2
x   y2
Definition: A parabola is the set of coplanar points that are the same distance from a fixed point (focus F), as they are
from a fixed line (Directrix d).
The focus is always “inside” the parabola and the directrix is
always “behind” the parabola.
NEW Parabola Equations:
Vertical:
 x  h
Horizontal:
y k
Vertex:
 h, k 
2
2
 4p y  k
 4 p  x  h
Find the vertex, focus, equation for directrix, and graph the parabola.
To graph extra points: Use 2 p from focal point.
32. y 2  8 x
Vertex:
Focus:
Directrix:
34. x 2  4 y
Vertex:
Focus:
Directrix:
38.
 y  1
2
 4  x  2 
Vertex:
Focus:
Directrix:
42. x 2  6 x  4 y  1  0
Vertex:
Focus:
Directrix:
Honors Pre-Calculus
9.2 Notes (Day 2)
Parabolas
Learning Targets: Students will be able to find the equation of a parabola and solve applied problems with parabolas.
Parabola Equations:
Vertical:
 x  h
Horizontal:
y k
Vertex:
 h, k 
2
2
 4p y  k
Old version: y  a  x  h   k
 4 p  x  h
Old version: x  a  y  k   h
2
2
Find the equation of the parabola described.
18. Focus = (-4, 0)
Vertex = (0, 0)
20. Focus = (0, -1)
Directrix: y = 1
28. Focus = (2, 4)
Directrix: x = -4
58. A cable TV receiver is in the shape of a parobloid of revolution. Find the location of the receiver (focus) if the dish is
six feet across and two feet deep.
Honors Pre-Calculus
9.3 Notes (Day 1)
Ellipses
Learning Targets: Students will be able to graph ellipses.
Definition of Ellipse - a set of coplanar points whose sum of the distance from two set points (foci) is constant.
Major Axis
Minor Axis
Vertices (V)
Center (C)
Foci (F)
Standard Equation of an Ellipse:
 x  h
a2
2
y k

b2
Center (h, k)
a = distance from center along the horizontal axis
b = distance from center along the vertical axis
c = distance from center to foci
c 2  a 2  b 2 or c 2  b 2  a 2
Find the center, vertices, foci, and then graph each ellipse.
Ex.
x2 y 2

1
25 81
2
1
16. 4 y 2  9 x 2  36
34.
 x  4
9
2
 y  2

4
2
1
42. x 2  9 y 2  6 x  18 y  9  0
Honors Pre-Calculus
9.3 Notes (Day 2)
Ellipses
Learning Targets: Students will be able to find the equation of an ellipse and solve applied problems with ellipses.
Find the equation of each ellipse described.
22. C = (0, 0) F = (0, 1) V = (0, -2)
26. F = (0, 2) & (0, -2) ; Length of the major axis = 8
48. F = (1, 2) & (-3, 2) V = (-4, 2)
54. C = (1, 2) V = (1, 4) Contains the point (2, 2)
58. Graph f ( x)   4  4 x 2
Honors Pre-Calculus
9.4 Notes (Day 1)
Hyperbolas
Learning Targets: : Students will be able to find the equation of a hyperbola and solve applied problems with
hyperbolas.
Definition of Hyperbola - a set of coplanar points the difference of whose distances from two fixed points (foci) is
constant.
Transverse Axis
Vertices (V)
Center (C)
Foci (F)
Standard Equation of an Ellipse:
 x  h
a2
2
y k

b2
2
1
or
y k
b2
2
 x  h

2
a2
1
Center (h, k)
a = distance from center along the horizontal
b = distance from center along the vertical
c = distance from center to foci
c2  a 2  b2
To find the asymptotes of the hyperbola, form the FUNDAMENTAL RECTANGLE using a and b
Equations of asymptotes:
If center @ (0, 0): y  
b
x
a
If center @ (h, k): y  k  
b
 x  h
a
Graph each hyperbola. Find the center, transverse axis, vertices, foci, and asymptotes.
20.
y 2 x2
 1
16 4
Ex. 4 x 2  25 y 2  100
40.
 y  3
4
2
 x  2

9
2
1
48. 2 x 2  y 2  4 x  4 y  4  0
42.
 x  4
2
 9  y  3  9
2
Honors Pre-Calculus
9.4 Notes (Day 2)
Hyperbolas
Learning Targets: : Students will be able to graph hyperbolas.
Find the equation of the hyperbola described.
12. C (0, 0) F (-3, 0) V (2, 0)
14. F (0, 6)
38. V (1, -3) & (1, 1)
54. Graph the function.
Asymptote: y  1 
3
 x  1
2
V (0, 2) & (0, -2)
f ( x)   9  9 x 2
Conic Sections
Shape
Vertical
Parabola
Horizontal
Parabola
Ellipse
Equation
 x  h
2
y k
 x  h
a
2
2
2
Graph
Special Features
 4p y  k
P-dist from V to F & d
V (h, k)
Extra points: +/- 2p from F
p > 0 up, p < 0 down
 4 p  x  h
P-dist from V to F & d
V (h, k)
Extra points: +/- 2p from F
p > 0 right, p < 0 left
y k

b
C (h, k)
a = horiz dist, b = vert dist
c = dist from C to F
2
1
2
c 2  a 2  b 2 or c 2  b 2  a 2
C (h, k)
Vertical
Hyperbola
 y k
Horizontal
Hyperbola
 x  h
Circle
(Not on test)
2
b2
 x  h

2
2
y k

2
a2
b2
 x  h   y  k 
2
2
a = horiz dist, b = vert dist
c = dist from C to F
1
a2
c2  a 2  b2
b
 x  h
a
b
fundamental rectangle 
a
asymp y  k  
Same as Vertical Hyperbola
1
 r2
C (h, k)
r = radius
a=b
Conic Sections
Shape
Vertical
Parabola
Horizontal
Parabola
Ellipse
Vertical
Hyperbola
Horizontal
Hyperbola
Circle
(Not on test)
Equation
Graph
Special
Features