Precalculus Home Enjoyment
Ch. 9A – Conic Sections
Date
11/2/2016
11/3/2016
11/4/2016
Day
Wednesday
Thursday
Friday
11/7/2016
Monday
11/8/2016
Tuesday
11/9/2016
Wednesday
11/10/2016
11/11/2016
11/14/2016
Objective
Circles
Parabolas
Parabola Lab
Home Enjoyment
Ch. 9A HW #1
Ch. 9A HW #2
Artist needs poster paper
Complete Parabola Lab
Ch. 9A HW #3
ELECTION DAY HOLIDAY
Ellipses
Ch. 9A HW #4
Thursday
Hyperbolas
Friday
Monday
Identifying Conics & Degenerate Cases
Halves of Conics
Ch. 9A HW #5, Study for Formula Quiz
Formula Quiz, Ch. 9A HW #6 and CTJ
Ch. 9A HW #7
11/15/2016
Tuesday
Review and HW Quiz
Ch. 9A HW #8, Study for Ch. 9A Test
11/16/2016
Wednesday
Test Part I
Day 1 of Ch. 9A Partner Test
Thursday
Test Part II
Day 2 of Ch. 9A Partner Test, Hand in LBB
Friday
Bouncing Ball Lab
Complete Lab Report
11/17/2016
#1
Circles
(A) Find the equation of the following circles:
(1) center (1,4) radius 3,
(2) center (-1,2) passing through the point (2,6),
(3) center (-3,-2) tangent to the x-axis
(4) Find the graphing form, center and radius of the following circle, graph and find x and y
intercepts: x2 + 6x + y2 – 2y = 6
(5) Find the equation of tangent lines to the circle (x-2)2 + (y+1)2 = 25 through the points on
the circle where y = 2.
(B) p. 643 Sec. 9.1 #41
Ans: (1) (x - 1)2 + (y - 4)2 = 9, (2) (x + 1)2+(y - 2)2 = 25, (3) (x + 3)2 + (y + 2)2 = 4
(4) (x + 3)2 + (y - 1)2 = 16, center (-3, 1) r= 4,
(5)
#2
( 0,1 ± 7 ) , ( −3 ±
15, 0
)
4
4
y − 2 = ( x + 2 ) and y − 2 =− ( x − 6 )
3
3
Parabolas.
(Don’t try to work like the textbook or the solution manual – they are very confusing!)
(Hint: Isolate the single variable first on all the equations, then match or graph.)
p. 643 Sec. 9.1 #43-48 all (Isolate the variable not squared, then match.),
• Find the vertex, focus, directrix, eccentricity and length of latus rectum. 63, 65, 71, 75
• Make a sketch of the information on a graph then find equation: 81. 83, 86, 87, 88, 89,
• Sketch the graph and find equation to answer questions: 99,103
#3
Parabola Lab Finish poster for lab.
#4
Ellipses
p. 653 Sec. 9.2 #9-12 all
• Make a sketch of the information on a graph then find equation: 13, 15, 19, 21, 23, 25,
• Find the center, vertices, foci, eccentricity and length of latus rectum: 31, 35, 39,
• Make a sketch of the information on a graph then find equation: 49, 51
• Sketch the graph and find equation to answer questions: 54, 55
• Find the center, vertices, foci, eccentricity, length of latus rectum, area, volume of the prolate ellipsoid and volume
of the oblate ellipsoid: 59. Explain both true and false: 63, 64
Precalculus Ch. 9A HW
(Ans: (59) ecc =
2
7
, LR = 4.5, Area = 12p, Vol. prolate ellipsoid = 48p, Vol. of oblate = 64 (56) T)
4
Bonus: (Work on loose leaf to be handed in for $3000) Use the definition of an ellipse to derive the
equation of an ellipse with foci (1, 1) and (–1, -1) and the sum of the focal radii equal 4.
(Hint: Use the distance formula from each foci to the point (x, y), the definition of ellipse, and some
algebra. No radicals in your answer.)
#5
Hyperbolas
p. 665 Sec. 9.3 # 7-10 all,
• Find the center, vertices, foci, equations of asymptotes, eccentricity and length of latus rectum: 25, 27, 29, 38
• Make a sketch of the information on a graph then find equation: 11, 13, 17, 47
• Sketch the graph and find equation to answer questions: 55, 56
Study for Formula Quiz: Graphing forms of equations of all conics (vertical and horizontal parabolas,
circles, ellipses and hyperbolas), formulas for eccentricity and latus rectums of all conics, areas of
circles and ellipses, volumes of spheres and both ellipsoids
#6
Identifying Conics and Degenerate Cases
p. 665 Sec. 9.3 #67-64 all (none of these are degenerate cases)
(A) Describe the graphs of the following equations
(2) y2 = -6,
(3) x2 + 6x + y2 + 8y= -25
(1) x2 = 4,
2
2
2
2
(5) (x-5) + 4y = 0, (6) 7x + 6y = -5
(4) x2 – 8x + y 2 = -25,
(Ans: (1) degenerate case of a parabola – the graph is two vertical lines x = 2 and x = -2, (2) degenerate case of a
parabola – no graph), (3) degenerate case of a circle = point (-3, -4), (4) degenerate case of a circle = no graph,
(5) degenerate case of an ellipse = point (5, 0), (6) degenerate case of an ellipse = no graph)
Critical Thinking Journal: (20 pts. – Choose one of the three attached “Sagas” and complete on that
sheet. Be creative and make them interesting for me to read! Everyone should have totally different
CTJ’s – don’t copy!!!!)
#7
Halves of Conics
Graph:
(1) =
x
4 + y2
(2) =
x
4 − y2
(3)=
x
3 4 − y2
(4)=
x
3 4− y
(5)=
y
x + 1
(6) y =
x +1
(7)
y = x +1
2
(8)
x = − 4−
y2
16
(9) y = − x
(10)
x=
(15) =
y
(16)
4 − x2
x=
− 9 − y2
y
(11)
y = x2 − 6
(12)
x=
− y + 25
(13) =
x
(14) y =
− x−4
4− y
(17) y =
− 4−
(18)
=
x
x2
4
y2
1−
9
Precalculus Ch. 9A HW
3
Ans:
(1)
(2)
(3)
(4)
#8
(9)
(14)
(10)
(15)
(11)
(16)
(12)
(17)
(13)
(18)
(5)
(6)
(7)
(8)
Study for Test: This is a two day partner test. You may use your graphing calculator on the whole
test. You may use one 4 X 6 note card with anything you want written on it. It may not be typed and
must be in your own handwriting. You must have it when you enter the classroom − no last minute
writing. This is a partner test, so you and your partner both must have a card and can have different
things on your note cards. Anyone without a card will take the test alone. You must staple the note card
to the test. Hand in Little Blue Book on Day 2 - Thursday.
Review:
Day 1 of Test:
I.
Identification of type of Conic as in HW #6
II. Equation Synthesis: Know what type of conic has certain eccentricities, latus rectums and
foci. Be able to create an equation using this basic information such as:
(1) Find the equation of a conic with eccentricity ½ with one vertex of major axis is at (0, 6)
and the length of the longest axis = 12.
(Ans: Many solutions for this ellipse, one of which is
x2
y2
+
=
1 .)
27
36
(2) Find the equation of the conic with eccentricity of 4/3, center at the origin and focus
at (8, 0) (Ans: Only one solution for this hyperbola,
x2 y 2
−
=
1 .)
36 28
III. Volumes of ellipsoids and area of ellipse
IV. Application Problem similar to those in HW #2, 4, 5
Precalculus Ch. 9A HW
4
Day 2 of Test:
V.
Graphing Analysis: Make sure you can (a) graph horizontal parabolas, (b) halves of conics such
as those in HW #7, and (c) complete the square to graph a conic and find its foci, sum or
difference in focal radii, length of latus rectum and eccentricity
(1) graph horizontal parabola x = −7y2 −12y,
(2) complete the square to graph the conic 9x2 − 18x − y2 + 8y = 88 and find its foci, sum or
difference in focal radii, length of latus rectum and eccentricity
(Ans:
( x − 1)
9
2
( y − 4)
−
81
2
asymptotes: y − 4 = ±3(x − 1), difference in focal radii = 6
VI.
Degenerate cases
(
1 , ecc = 10 , Latus Rectum =54, Foci = 1 ± 90, 4
=
)
,
Precalculus Ch. 9A HW
5
Objective: To draw a real life parabola and find its characteristics.
Materials: ¼ piece of poster board per group, colored pencils, markers or crayons, ruler (Do your
math in your notebook before transferring it to the poster board.)
Group Assignments: Artist, Reader (initial steps), Mathematician
Directions: Each group will be assigned a water fountain on campus to measure the arch of water
(use rulers, yard sticks, or any other means necessary to measure the arch in Centimeters.
_____ Measure all the distances at the same time. Remember you need at least three points for
the regression equation.)
_____ Make sure Mrs. Disher takes your group’s picture doing the measuring.
_____ After making the measurements, determine graph (decide where you want the axis of
symmetry and both axis must be the same scale – specify the scale and draw to scale), the
equation of the parabola, the restricted domain, vertex, axis of symmetry, focus,
directrix, eccentricity, and length of latus rectum. (round all numbers 1 place behind the
decimal)
_____ Reader: Double check that everything in the rubric is on the final product.
Grading Rubric: The following information must be on the poster board. Everything must be in
color – be creative)
1 pt.
7 pts.
Rough sketch on the back of the poster board with the measurements you took
On the front of the poster board print a creative title (keep it clean), the location of
the water fountain, the names of group members, the title of class (Precalculus), date,
your hour, teacher’s name, and paste your group picture
20 pts.
Sketch of the following (to scale) on the front of the poster board:
• the x and y axis and units of measure (to scale)
• the parabola (only the portion that represents the flow of the water, labeled with
name, equation)
• vertex (labeled with name and ordered pair)
• domain and range in interval notation (restricted to only the portion that represents
the flow of the water)
• the latus rectum (sketched accurately to scale labeled with name and length)
• eccentricity (labeled with name and value)
• the focus (located and labeled with name and ordered pair)
• the axis of symmetry and directrix (sketched and labeled with name and equations)
2 pts.
Neatness and originality
Total: 30 pts
Precalculus Ch. 9A HW
6
Little Blue Book of PreCalculus Properties
Ch. 9A – Conic Sections
9A-1
Conic sections (what is a conic section and why is it called that, definition of a conic
involving a plane, picture of each slicing a cone)
9A-2 Circle (def., 2 equations - standard form and graphing form, graph, eccentricity,
latus rectum, area, circumference, real life examples)
9A-3 Parabola (def., 2 forms of equation, finding vertex from each eq., graph, vertical and
horizontal graphs & equations, directrix, axis of symmetry, focus, ecc., L.R.,)
9A-4 Real life parabolas (discuss and draw the reflective property of a parabola and what it is
used for)
9A-5 Ellipse (def., 2 eq., standard form and graphing form graph, foci, vertices, major &
minor axes, relationship of a, b, & c, eccentricity, latus rectum, area, def and volume
of prolate ellipsoid, definition and volume of oblate ellipsoid)
9A-6 Real World Ellipses (discuss and draw the reflective property of an ellipse and how it
relates to a whisper chamber, discuss earth’s orbit about the sun, define apogee and
perigee)
9A-7 Hyperbola (def., 2 eq. standard form and graphing form, graph, how can you tell
which way it opens, vertices, transverse & conjugate axes, relationship of a, b, & c,
foci, asymptotes, ecc., L.R.)
9A-8 Real World Hyperbolas (discuss and draw the reflective property of a hyperbola and
how used in real life)
9A-9 Eccentricity (2 definitions, formulas and examples of each conic, picture with
directrix and eccentricity values – you can tape a picture in LBB, what eccentricity
tells about a conic graph)
9A-10 Latus Rectum (definition of focal chord, definition of latus rectum, formulas and
examples with picture of each conic, picture of the LR in each conic, why used)
9A-11 Degenerate cases of conics (equation ex. of each and picture representations from
cones- you can print out a picture)
9A-12 Root/radical functions (example worked out and graphed of  parabola,  circle, 
ellipse,  hyperbola, how to determine which half, domains and ranges of each example)
Precalculus Ch. 9A HW
Ch. 9A Conics
Critical Thinking Journal (20 pts)
7
Name
Date:
Saga of the
Roaming Ellipse
You are an ellipse- give yourself a name.
Your owner is a Precalculus student who moves you and stretches
you. Using all you know about yourself, describe what is happening
to you while the Precalculus student is doing his/her homework.
You must include ten facts or properties of an ellipse in your discussion.
(Write in paragraph form but number the ten facts. (ex. , , , …)
Hr:
Precalculus Ch. 9A HW
8
Ch. 9A Conics
Critical Thinking Journal (20 pts)
Name
Date:
Saga of the Roaming Hyperbola
Hr:
You are a hyperbola- give yourself a name.
Your owner is a Precalculus student who moves you and stretches you. Using all you know about yourself,
describe what is happening to you while the Precalculus student is doing his/her homework.
You must include ten facts or properties of a hyperbola in your discussion.
(Write in paragraph form but number the ten facts. (ex. , , , …)
Precalculus Ch. 9A HW
9
Ch. 9A Conics
Critical Thinking Journal (20 pts)
Name
Date:
Saga of the Roaming Parabola
Hr:
You are a parabola- give yourself a name.
Your owner is a Precalculus student who moves you and stretches you.
Using all you know about yourself, describe what is happening to you while the Precalculus student is doing
his/her homework. You must include ten facts or properties of a parabola in your discussion.
(Write in paragraph form but number the ten facts. (ex. , , , …)