Precalculus
Quarter 3 Project: Conic Sections
Name _________________________________________
The objective of this project is to expose students to conic sections in an independent study format. Little
to no class time will be allotted for this project which is due at the beginning of class on Friday, March 1.
Students should save a copy of the project packet and turn in a completed packet (in a binder or a folder
with clips). All work for this project will be completed individually.
I. Overview
____ / 6 pts
1. Read the “History of Conic Sections” on the JWilson Site. Which mathematician is given credit for
‘discovering’ conic sections? _________________________ What three famous problems was he
attempting to solve using conics?
a. _________________________________
b. _________________________________
c. _________________________________
2. Watch the Brighton Introductory Video. (Use ear buds/headphones.) Answer the following
questions as you’re watching. (2-minute video)
a. Why are conic sections called “conic sections”? ________________________
________________________________________________________________
b. What are the four conic sections, and how is each created? (You may also want to visit this
web page (http://math.about.com/library/blconic.htm) for diagrams of the conic sections.)
i. __________________________________________________________
ii. __________________________________________________________
iii. __________________________________________________________
iv. __________________________________________________________
3. One of the prerequisite skills that you will need to have to work with conic sections is completing
the square. Go to http://www.purplemath.com/modules/sqrquad.htm . As you are reading the
examples, provide the work for the problems below. (You only need to read page 1.)
a. Find the x-intercepts of y = 4x2 – 2x – 5.
b. Solve x2 + 6x – 7 = 0 by completing the square.
b. Write instructions for a friend for how to solve 3x2 – 6x – 9 = 0 by completing the square.
c.
Have a classmate follow your instructions. If he/she does not get the correct answers {3, 1}, revise your instructions below. If he/she does get the correct answer, draw a smiley
face.
d. We will sometimes need to complete the square for several different variables. (Make sure
you understand this example.)
4 x2  y 2  8x  4 y  4  0
4 x 2  8 x  y 2  4 y  4
4( x 2  2 x)  ( y 2  4 y )  4
4( x  1) 2  ( y  2) 2  4  4  4
4( x  1) 2  ( y  2) 2  4
( x  1) 2 ( y  2) 2

1
1
4
II. Instruction
_____ / 34 pts
Go to www.pearsonsuccessnet.com. Login with the username/password on your 'parent letter'. Then, go to the
"To Do" section to complete your online assignments. Watch the introductory video first. Then, watch each
section's video prior to working on that material. When you open each section, you will find tabs for Launch,
Instruction, Practice, and Self-Assessment. You need to go through each section except for the Practice. Record
your answers for the Self-Assessment below as well as your score. Include all appropriate WORK.
Section 10.1 Self-Assessment
1.
2.
3. a. __________________
Score: ____ / 5
Section 10.2 Self-Assessment
1.
2.
3.
4.
5.
Score: _____ / 5
Section 10.3 Self-Assessment
1.
b. _________________ c. ________________
2.
3.
4.
5.
Score: _____/5
Section 10.4 Self-Assessment
1.
2.
3.
4.
Score: _____ / 4
Section 10.5 Self-Assessment
1.
2.
3.
Score: ___ / 3
Section 10.6 Self-Assessment
1.
2.
3.
4.
Score: ___ / 4
End-of-Chapter MathXL Assessment (You may want to refer to the enclosed formula sheet.)
1.
2.
3.
4.
5.
6.
7.
8.
Score: ___ / 8
III. End-of-Unit Assessment: Complete the unit assessment posted on the teacher's webpage. Print the test and
include it after this page in your packet. You may use only non-human resources.
_____ / 24 pts
IV. Choose one of the following extensions to complete.
_____ / 26 pts.
Organize the work for each project on a standard-sized poster sheet. Points will be deducted for sloppy and/or
missing work. Include a title for your poster.
A. Clowning Around with Conics
1. Find and print 4 pictures of clown faces which each depict a different emotion. Label the emotion. Cite
your sources.
2. Design a clown face using graphs (or parts of graphs) of conic sections (circles, ellipses, parabolas,
hyperbolas). The face should convey a specific emotion (anger, sadness, joy, surprise, etc.) Graph the face
on a sheet of graph paper (if your poster board has a grid on it, you can graph directly on the poster). List
the equations you used and any restrictions, i.e. x2 +y2=4, -2<x<2. Add color. You must use at least 3
different types of conic sections in your design.
3. Graph your equations on your graphing calculator also. Ask Mrs. S. to connect your calculator to her
computer, so you can print out the equations and the graph.
B. Did you see that conic?
1. Take a picture of at least three different conics (circle, parabola, ellipse, or hyperbola) that you find. See
the Prezi at http://prezi.com/y24ohsfoqgta/conic-sections-around-us/ for ideas.
2. Print each picture for your poster. Overlay a coordinate grid over your photo. Draw coordinate axes over
your photo. Highlight the conic section in the photo with a marker so that it stands out.
3. Find the equation of each conic section. Show all work.
V. Above and Beyond
_____ / 10 pts
Suggestions: If you've chosen Option A, wear your clown-face design and take a picture to include on your
poster; if you wear it to school, I'll give you bonus points  You can look online for homemade recipes for clown face
paint. If you've chosen Option B, include all four conics on your poster. Create "Section VI" for this project, making
sure that you include directions, sample work, and an answer key if appropriate.
Total Project Grade:
_____ / 100 pts.
Resource: Pre Calculus Conic sections formula sheet:
Parabola Information
Vertical Axis
Horizontal axis
equation
(x-h)2=4p(y-k)
(y-k)2=4p(x-h)
Axis of symmetry
x=h
y=k
Vertex
(h,k)
(h,k)
Focus
(h,k+p)
(h+p,k)
Directrix
y=k-p
x=h-p
Direction of opening
p>0 then up; p<0 then down
p>0 then rignt; p<0 then left
Vertical Major Axis
Horizontal Major axis
 x  h 2   y  k 2
 x  h 2   y  k 2
Ellipse Information
equation
b2
a2
1
a2
center
(h,k)
(h,k)
Vertices
(h,k±a)
(h±a,k)
Foci
(h,k±c)
(h±c,k)
Major axis equation
2a=length of major axis
Minor axis equation
2b=length of minor axis
Equation that relates a, b, and c
a2=b2+c2
Eccentricity of an ellipse
e=(c/a)
b2
1
Hyperbola Information
Vertical Transverse Axis
Horizontal Transverse axis
 y  k  2   x  h 2
equation
a2
b2
1
 x  h  2   y  k 2
a2
b2
center
(h,k)
(h,k)
Vertices
(h,k±a)
(h±a,k)
Foci
(h,k±c)
(h±c,k)
Assymptote equation
yk
Equation relating a, b, and c
c2=a2+b2
a
x  h 
b
yk
1
b
x  h 
a
Line Information
equation
y=mx+b or Ax+By+C=0
slope
m=tanθ
Angle between two lines
tan  
Distance between a point and a
line
Classifying conic
sections
Ax2+Cy2+Dx+Ey+F=0
d
m2  m1
1  m1m2
Ax1  By1  C
A2  B 2
Circles
Parabola
Ellipse
Hyperbola
A=C
AC=0, Both
are not 0
AC>0
AC<0