Precalculus: Chapter 9 “Conic Sections” Practice Guide
Ms. Tyler’s office hours: 2 (STEM), 5,8,9
Day
Topic
1
Circle
2
Parabolas
3
Circle &
Parabola
5
Ellipse
6
Hyperbola
8
Practice
W rite the equation of a circle
Graph and analyze a circle
Determine the radius and center of a circle
Graph and analyze vertical and horizontal
parabolas
Worksheet #1
(1,3,5,7,9,11)
Review &
 Solve parabolic application problems
Applications
4
7




Learning Targets and
Assessments
Ellipse &
Hyperbola
Conic
Recognition
CIRCLE & PARABOLA QUIZ
Worksheet #2
(1,3,5,7,9,11,12)
Worksheet #3
ALL
TBD
ELLIPSE & HYPERBOLA QUIZ
Worksheet #5
(1,3,5,7,9–13)
Worksheet #6
(1,3,5,7,9,10)
Worksheet #7
ALL
Worksheet #8
ALL
 Graph and analyze an ellipse
 Graph and analyze a hyperbola
Review Ellipse & Hyperbola (Prepare for
Quiz)
9
Review
Review Conic Sections
Review Packet
10
Review
Review Conic Sections
Study!
11
***CONICS ASSESSMENT***
*This is an outline. The practice/quizzes/tests are subject to change*
PreCalculus – Unit 9
Name
DAY 1 Notes – “The Circle”
Date
Period
Standard form of a circle
We need the
and
to determine the equation of a circle.
Learning Target: Write the equation of a circle.
EX 1) Write the equation of a circle with center at (3, –7) and a radius of length 7 .
EX 2) Write the equation of a circle with center at (– 2, 0) and a radius of length 4.
Remember…
Distance Formula
Midpoint Formula
EX 3) The two given points (9, 2) ( 3, 4) are endpoints of a diameter of a circle. Write the equation of
the circle in standard form.
EX 4) Find the equation of the circle shown below.
(3, 2)
( 6, 6)
Learning Target: Graph and analyze a circle.
EX 5) Sketch the following circle:
EX 6) Sketch the following circle:
( x  3)2  ( y  2)2  9
Center:
x 2  ( y  3)2  16
Radius:
Center:
Radius:
Learning Target: Determine the radius and center of a circle.
Find the center and the radius of the given circle.
EX 7) x 2  6 x  y 2  12 y  9  0
EX 8) x 2  y 2  6 x  4 y  12
Center:
Center:
Radius:
DAY 1 Practice: Worksheet #1 – The Circle #(1, 3, 5, 7, 9, 11)
Radius:
PreCalculus – Unit 9
Name
Worksheet #1 – The Circle (1, 3, 5, 7, 9, 11)
Date
Period
Learning Target: Write the equation of a circle.
Write the equation for each circle in standard form given the following information.
1. Center at  3, 2 and tangent to the x-axis.
2. Center at 1,4  and radius of 3.
The two given points are endpoints of a diameter of the circle. Write the equation of the circle in
standard form.
3.  4,3 and  4, 3
4.



5. 5,7 and 13, 1
6.
3, 5 and  7,2
2,  5 and 3 2,4 5

Learning Target: Graph and analyze a circle.
Sketch each circle.
2
7.  x  1  y 2  36
8.
 x  4    y  3
2
2
4
Learning Target: Determine the radius and center of a circle.
Find the center and radius of the following circles.
9. x 2  6x  y2  8 y  9  0
Center:
10. x 2  4x  y2  12 y  4
Radius:
11. x 2  y2  4x  6 y  12  0
Center:
12. x 2  y2  2x  4 y  4
Radius:
Center:
Radius:
Center:
Radius:
PreCalculus – Unit 9
Name
DAY 2 Notes – “The Parabola”
Date
Period
Learning Target: Graph and analyze vertical and horizontal parabolas.
VERTICAL PARABOLA
VERTEX
FORM
STANDARD
FORM
Positive “a” 
Negative “a”
HORIZONTAL PARABOLA
Positive “a” 
Vertex
Vertex
h=
h=
k=
k=
Vertex
Vertex
Negative “a”
Graph the following parabolas. Identify the vertex, axis of symmetry, domain, and range for each.
EX 1) y   x  3  4
EX 2) y   x 2  4x  2
Vertex:
Vertex:
Domain:
Domain:
Range:
Range:
Axis of Symmetry:
Axis of Symmetry:
2
EX 3) x  ( y  3)2
EX 4) x  3( y  1)2  2
Vertex:
Vertex:
Domain:
Domain:
Range:
Range:
Axis of Symmetry:
Axis of Symmetry:
EX 5) x   y2  6 y  6
Vertex:
Domain:
Range:
Axis of Symmetry:
EX 6) The revenue of a bus company depends on the number of unsold seats. If the revenue R is given by
R  5000  50 x  x 2 , where x is the number of unsold seats, find the maximum revenue and the
number of unsold seats that maximizes the revenue.
DAY 2 Practice: Worksheet #2 – The Parabola #(1, 3, 5, 7, 9, 11, 12)
PreCalculus – Unit 9
Name
Worksheet #2 – The Parabola (1, 3, 5, 7, 9, 11, 12)
Date
Period
Learning Target: Graph and analyze vertical and horizontal parabolas.
Graph the following parabolas. Identify the vertex, axis of symmetry, domain, and range for each.
1.
y  2 x  3  2
2
2.
y   x  2
2
Vertex:
Vertex:
Domain:
Domain:
Range:
Range:
Axis of Symmetry:
Axis of Symmetry:
3.
y  x 2  2x  3
4.
y  2x 2  4x  5
Vertex:
Vertex:
Domain:
Domain:
Range:
Range:
Axis of Symmetry:
Axis of Symmetry:
5.
x  2 y  3  1
2
6.
x   y  1
2
Vertex:
Vertex:
Domain:
Domain:
Range:
Range:
Axis of Symmetry:
Axis of Symmetry:
7.
x  y2  2 y
8.
x  2 y2  2 y  3
Vertex:
Vertex:
Domain:
Domain:
Range:
Range:
Axis of Symmetry:
Axis of Symmetry:
9.
x  2 y2  8 y  5
10.
x  3 y2  30 y  73
Vertex:
Vertex:
Domain:
Domain:
Range:
Range:
Axis of Symmetry:
Axis of Symmetry:
Learning Target: Write the equation of a circle.
11. Write the equation of the circle shown below.
(1, 6)
(7, 2)
Learning Target: Determine the radius and center of a circle.
x 2  y 2  6x  4 y  9  0
12. Find the center and radius of the following circle.
Center:
Radius:
PreCalculus – Unit 9
Name
DAY 3 Notes – “Parabola Applications”
Date
Period
WARM-UP:
1) Determine if the given equation is a parabola or a circle?
x 2  3x  y  5
circle
parabola
2) Find the equation of the circle shown below.
(10,10)
(2, 5)
Center:
Radius:
Equation:
Learning Target: Solve parabolic application problems.
EX 1) MCC wants to construct a rectangular parking lot on land bordered on one side by a highway. It
has 320 feet of fencing with which to fence off the other three sides. What should be the dimensions of
the lot if the enclosed area is to be maximizes?
EX 2) The culvert (as shown) is shaped like a parabola. If it is 8 inches wide at the base and 64 inches
high, how wide is the arch 16 inches from the ground?
EX 3) A skateboard half pipe is 18 ft wide at the top and the decks are 20 ft high off the ground. How
wide is the half pipe 6 ft from the bottom?
EX 4) Let’s pretend that the arch of St. Louis is a parabola. (Although the arch looks like a parabola it is
really a catenary curve- google it). An aerobatic pilot would like to fly her plane under the arch. Would
this be possible for her to do without touching it?
Additional information needed:
 The height of the arch is 630’.
 The width at the base is also 630’.
 The wing span of the plane is 20’.
 The legal minimum elevation that a plane is allowed to fly is 500’
above the surface.
DAY 3 Practice: Worksheet #3 – ALL
PreCalculus – Unit 9
Name
Worksheet #3 – Circle/Parabola Review (ALL)
Date
Period
Learning Target: Solve parabolic application problems.
1. A culvert is shaped like a parabola, 6 ft across the top and 27 ft deep. How wide is the culvert 15 ft
from the top?
2. The number of mosquitoes, M, in millions, in a certain area of Kentucky depends on the June rainfall, x,
in inches, is approximately as follows M  10x  x 2 . Find the rainfall that will produce the maximum
number of mosquitoes. What is the maximum number of mosquitoes?
Learning Target: Write the equation of a circle.
3. Given points P (11, 13) and Q (-7, -11) are endpoints of a diameter of a circle.
Find the equation of the circle in standard form.
Learning Target: Graph and analyze a circle.
4. Write the equation of the circle whose center is (-4, 2) and radius is 3.
Sketch the graph.
Learning Target: Determine the radius and center of a circle.
5. Given the circlex 2  y 2  4 x  12 y  4  0, identify the center and radius.
Learning Target: Graph and analyze vertical and horizontal parabolas.
Graph the parabolas. Identify the vertex, axis of symmetry, domain, and range of each.
6.
y  2 x2  4 x  5
7.
x  2 y 2  4 y  4
Vertex:
Vertex:
Domain:
Domain:
Range:
Range:
Axis of Symmetry:
Axis of Symmetry:
8.
1
y   ( x  3) 2  1
4
9.
x  3( y  1)2  3
Vertex:
Vertex:
Domain:
Domain:
Range:
Range:
Axis of Symmetry:
Axis of Symmetry:
PreCalculus – Unit 9
Name
DAY 5 Notes – “The Ellipse”
Date
Period
Learning Target: Graph and analyze an ellipse.
Ellipse- Set of coplanar points, the __________ of whose distances from 2 fixed points is _______________.
*the fixed points are called
.
F=
C=
V=
E=
Major axis-
Minor axis-
EQUATION OF ELLIPSE:
Center = __________________
“a” is always______________________
“b” is always______________________
Directions: Sketch the graph of each of the following ellipses.
EX 1)
x2 y 2

1
16 9
Center:
Vertices:
Endpoints:
Domain:
Range:
( x  3)2 ( y  2) 2

1
9
4
EX 2)
2.
EX 3)
25x2  9 y 2  225
25x2  9 y 2  225
Center:
Center:
Vertices:
Vertices:
Endpoints:
Endpoints:
Domain:
Domain:
Range:
Range:
EX 4) Find the equation of an ellipse whose center is (0, 0), vertex (6, 0), and minor axis has a length of 8.
EX 5) Find the equation of an ellipse whose center is (-1, -2), length of minor axis is 4, vertex (-1, 1).
DAY 5 Practice: Worksheet #5 – The Ellipse #(1,3,5,7,9-13)
PreCalculus – Unit 9
Name
Worksheet #5 –The Ellipse (1,3,5,7, 9 –13)
Date
Period
Learning Target: Graph and analyze an ellipse.
Directions: Sketch the graph of each of the following ellipses. Identify the information requested.
1.
3.
( x  1) 2 ( y  3) 2

1
9
25
2.
x2 y 2

1
9 4
Center:
Center:
Vertices:
Vertices:
Endpoints:
Endpoints:
Domain:
Domain:
Range:
Range:
x2  4 y 2  16
4.
x2 y 2

1
6 9
Center:
Center:
Vertices:
Vertices:
Endpoints:
Endpoints:
Domain:
Domain:
Range:
Range:
Directions: Write an equation for each of the following ellipses.
5. Ellipse, center at the origin, length of major axis is 12, endpoint of minor axis at (0, 4)
6. Ellipse, center at the origin, vertex (6,0), length of minor axis is 8
7. Ellipse, center at (2, -2), a = 4, b = 3, major axis parallel to the x-axis.
8. Ellipse, center at (-1, -2), length of minor axis is 4, vertex (-1,1)
Learning Target: Graph and analyze vertical and horizontal parabolas.
9. Study the graph and determine the equation of the parabola.
A. x  ( y  1)2  4
B. x  ( y  4)2  1
C. y  ( x  4)2  1
D. y  ( x  1)2  4
E. I would be guessing if I circled one above.
Learning Target: Write the equation of a circle.
10. The two given points are endpoints of a diameter of the circle. Write the equation of the circle in
standard form  3,6  and  4,8 
Learning Target: Identify an equation as a circle, parabola, ellipse, or hyperbola.
________11. y  3x 2  x  8
A. circle
________12. y 2  x 2  x  2 y  8
B. parabola
________13. 4 y 2  3x 2  x  2 y  8
C. ellipse
PreCalculus – Unit 9
Name
DAY 6 Notes – “The Hyperbola”
Date
Period
WARM-UP:
 x  3
2
Graph the following:
16

y2
1
49
Center:
Vertices:
Endpoints:
Domain:
Range:
Learning Target: Graph and analyze a hyperbola.
Hyperbola- Set of coplanar points, the
(foci) is _______________.
of whose distances from 2 fixed points
Directions: Sketch the graph of each of the following hyperbolas.
EX 1)
( y  5) 2 ( x  1) 2

1
4
9
Center:
Vertices:
Domain:
Range:
EX 2) 4 x 2  y 2  16
Center:
Vertices:
Domain:
Range:
EX 3) Find the equation of a hyperbola whose center is (-3, 1), a = 4, b = 2, transverse axis is parallel to xaxis.
DAY 6 Practice: Worksheet #6 – The Hyperbola #(1,3,5,7,9,10)
PreCalculus – Unit 9
Name
Worksheet #6 –The Hyperbola (1,3,5,7,9,10)
Date
Period
Learning Target: Graph and analyze a hyperbola.
Directions: Sketch the graph of each of the following hyperbolas.
1.
( x  3)2 ( y  2) 2

1
16
49
2.
( y  1)2 ( x  3)2

1
25
36
Center:
Center:
Vertices:
Vertices:
Domain:
Domain:
Range:
Range:
3. 25 x 2  4 y 2  100
4. x 2  9  y 2
Center:
Center:
Vertices:
Vertices:
Domain:
Domain:
Range:
Range:
5. 4 x 2  y 2  16
6.
x2 y 2

1
8 12
Center:
Center:
Vertices:
Vertices:
Domain:
Domain:
Range:
Range:
Directions: Write an equation for each of the following hyperbolas.
7. Hyperbola, center at (-3, 1), a = 4, b = 2, transverse axis parallel to the y-axis
8. Hyperbola, center at (4, 3), vertex (1, 3), b = 2
Learning Target: Graph and analyze vertical and horizontal parabolas.
Graph the parabola. Identify the vertex, axis of symmetry, domain, and range of each.
9.
x   y 2  6 y  11
Vertex: ____________________________
Domain: ___________________________
Range: __________________
__________
Axis of symmetry: _________ __________
Learning Target: Graph and analyze an ellipse.
Graph the parabola. Identify the center, endpoints, vertices, domain, and range.
10.
( x  4) 2 ( y  2) 2

1
1
16
Center:
Vertices:
Endpoints:
Domain:
Range:
PreCalculus – Unit 9
Name
Conic Recognition
Date
Period
Learning Target: Identify an equation as a circle, parabola, ellipse, or hyperbola.
Identify the following shape according to the given equation.
 x  h   y  k 
2
 x  h
a2
2
2
y k

b2
 r2
2
1
y  a  x  h  k
x  a y  k  h
2
 x  h
a2
2
y k

b2
2
 y k
2
1
b2
2
 x  h

a2
2
1
Identify the following shape. Rewrite each equation into standard or vertex form by completing
the square to determine the center or vertex point.
1. x  6 y  3 y 2  2
1.
Center/Vertex
A. circle
B. vertical parabola
C. horizontal parabola
( x  3)2 ( y  2) 2

1
2.
16
16
D. ellipse
E. hyperbola
2.
Center/Vertex
A. circle
B. vertical parabola
3. x 2  4 x  4 y 2  8 y  4  0
C. horizontal parabola
D. ellipse
3.
Center/Vertex
E. hyperbola
A. circle
B. vertical parabola
C. horizontal parabola
4. y 2  4 x 2  4 y  8x  4  0
D. ellipse
E. hyperbola
4.
Center/Vertex
A. circle
B. vertical parabola
C. horizontal parabola
5. 25x2  4 y 2  100
D. ellipse
E. hyperbola
5.
Center/Vertex
A. circle
B. vertical parabola
C. horizontal parabola
6. x 2  2 y
D. ellipse
E. hyperbola
6.
Center/Vertex
A. circle
B. vertical parabola
C. horizontal parabola
7. 4 x 2  y 2  24 x  4 y  16  0
D. ellipse
E. hyperbola
7.
Center/Vertex
A. circle
B. vertical parabola
8. x 2  y 2  8x  12 y  3  0
C. horizontal parabola
D. ellipse
8.
Center/Vertex
E. hyperbola
A. circle
B. vertical parabola
PreCalculus – Unit 9
C. horizontal parabola
Worksheet #8 –Conic Recognition (ALL)
D. ellipse
Name
E. hyperbola
Date
Period
Identify the following as a circle, parabola, ellipse, or hyperbola. Circle your answer.
1. x 2  3x  y 2  2 y  8
A. circle
B. parabola
C. ellipse
D. hyperbola
2. y 2  3 y  3x  4
A. circle
B. parabola
C. ellipse
D. hyperbola
3. x 2  2 y 2  2 x  4 y  12
A. circle
B. parabola
C. ellipse
D. hyperbola
4. 5 x 2  4 y 2  2 x  12
A. circle
B. parabola
C. ellipse
D. hyperbola
5. x 2  y 2  6 x  4 y  9
A. circle
B. parabola
C. ellipse
D. hyperbola
6. x  10 y 2  4 y  1
A. circle
B. parabola
C. ellipse
D. hyperbola
7. 2 y 2  5 x 2  7 x  8
A. circle
B. parabola
C. ellipse
D. hyperbola
8. y 2  3x 2  1  5 x
A. circle
B. parabola
C. ellipse
D. hyperbola
9. 5x2  5 y 2  5x  6 y  5
A. circle
B. parabola
C. ellipse
D. hyperbola
10.  x 2  y 2  3x  y  12
A. circle
B. parabola
C. ellipse
D. hyperbola