Post on 21-Jan-2016
Chapter 8: Test Your Proficiency
8-2 Parabolas
8-3 Circles
8-4 Ellipses
8-5 Hyperbolas
8-6 Identifying Conic Sections
Directions: •Select a section to work on.•Work out each problem on a piece of paper. •Click to check your answer.•For detailed steps click on the provided link.•Move on to the next problem or return to the menu.
8-2 Parabolas
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2
1. Write the equation of the parabola in standard form.
3 6 12y x x
8-2 Parabolas
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2
1. Write the equation of the parabola in standard form.
3 6 12y x x
23 1 9y x
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8-2 Parabolas
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2
1. Write the equation of the parabola in standard form.
3 6 12y x x
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8-2 Parabolas
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2
2. Write the equation of the parabola in standard form.
2 12 1x y y
8-2 Parabolas
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2
2. Write the equation of the parabola in standard form.
2 12 1x y y
22 3 19x y
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8-2 Parabolas
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2
2. Write the equation of the parabola in standard form.
2 12 1x y y
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8-2 Parabolas
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2
3. Write the equation of the parabola in standard form.
8 4x y y
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2
3. Write the equation of the parabola in standard form.
8 4x y y
24 20x y
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8-2 Parabolas
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2
3. Write the equation of the parabola in standard form.
8 4x y y
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8-2 Parabolas
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2
4. Identify all of the characteristics of the parabola:
vertex, direction of opening, axis of symmetry, focus,
directrix, and length of the latus rectum.
2 3 1x y
8-2 Parabolas
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2
4. Identify all of the characteristics of the parabola:
vertex, direction of opening, axis of symmetry, focus,
directrix, and length of the latus rectum.
2 3 1x y
1vertex: 1, 3 focus: 1 , 3
8
7opens right directrix:
81
axis: 3 latus rectum: unit2
x
y
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8-2 Parabolas
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2
4. Identify all of the characteristics of the parabola:
vertex, direction of opening, axis of symmetry, focus,
directrix, and length of the latus rectum.
2 3 1x y
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8-2 Parabolas
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2
5. Identify all of the characteristics of the parabola:
vertex, direction of opening, axis of symmetry, focus,
directrix, and length of the latus rectum.
24 5
3y x
8-2 Parabolas
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2
5. Identify all of the characteristics of the parabola:
vertex, direction of opening, axis of symmetry, focus,
directrix, and length of the latus rectum.
24 5
3y x
5vertex: 4, 5 focus: 4,4
8
3opens down directrix: 5
83
axis: 4 latus rectum: units2
y
x
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8-2 Parabolas
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2
5. Identify all of the characteristics of the parabola:
vertex, direction of opening, axis of symmetry, focus,
directrix, and length of the latus rectum.
24 5
3y x
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8-2 Parabolas
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236. Graph the parabola: 1 3
2y x
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236. Graph the parabola: 1 3
2y x
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8-2 Parabolas
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236. Graph the parabola: 1 3
2y x
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8-2 Parabolas
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27. Graph the parabola: 2 2 3x y
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27. Graph the parabola: 2 2 3x y
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8-2 Parabolas
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27. Graph the parabola: 2 2 3x y
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8-2 Parabolas
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8. Write an equation for the parabola with vertex
at 3,5 and focus at 3,1 .
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8. Write an equation for the parabola with vertex
at 3,5 and focus at 3,1 .
213 5
16y x
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8-2 Parabolas
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8. Write an equation for the parabola with vertex
at 3,5 and focus at 3,1 .
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8-3 Circles
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2 2
1. Write the equation of the circle in standard form.
10 8 6 0x y x y
8-3 Circles
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2 2
1. Write the equation of the circle in standard form.
10 8 6 0x y x y
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2 25 4 47x y
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8-3 Circles
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2 2
1. Write the equation of the circle in standard form.
10 8 6 0x y x y
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8-3 Circles
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2 2
2. Identify the center and radius of the circle.
5 2 18x y
8-3 Circles
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2 2
2. Identify the center and radius of the circle.
5 2 18x y
Center 5, 2 ; radius = 3 2 units
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8-3 Circles
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Step 1: 2 2
2. Identify the center and radius of the circle.
5 2 18x y
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8-3 Circles
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3. Write an equation of the circle with a diameter
having endpoints 5, 6 and 3, 8 .
8-3 Circles
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3. Write an equation of the circle with a diameter
having endpoints 5, 6 and 3, 8 .
2 24 7 2x y
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8-3 Circles
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3. Write an equation of the circle with a diameter
having endpoints 5, 6 and 3, 8 .
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8-3 Circles
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2 24. Graph the circle: 4 2 12x y
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2 24. Graph the circle: 4 2 12x y
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8-3 Circles
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2 24. Graph the circle: 4 2 12x y
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8- 4 Ellipses
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2 2
1. Write the equation of the ellipse in standard form.
5 4 20 8 4 0x y x y
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8- 4 Ellipses
2 2
1. Write the equation of the ellipse in standard form.
5 4 20 8 4 0x y x y
2 22 1
14 5
x y
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8- 4 Ellipses
2 2
1. Write the equation of the ellipse in standard form.
5 4 20 8 4 0x y x y
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8- 4 Ellipses
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2 2
2. Identify the center and foci and the lengths of
the major axis and minor axis for the ellipse.
3 11
25 4
x y
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8- 4 Ellipses
2 2
2. Identify the center and foci and the lengths of
the major axis and minor axis for the ellipse.
3 11
25 4
x y
Center: 3, 1
Foci: 3 21, 1 , 3 21, 1
Major axis = 10 units
Minor axis = 4 units
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8- 4 Ellipses
2 2
2. Identify the center and foci and the lengths of
the major axis and minor axis for the ellipse.
3 11
25 4
x y
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8- 4 Ellipses
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2 2
3. Identify the center and foci and the lengths of
the major axis and minor axis for the ellipse.
5 81
16 49
x y
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8- 4 Ellipses
2 2
3. Identify the center and foci and the lengths of
the major axis and minor axis for the ellipse.
5 81
16 49
x y
Center: 5, 8
Foci: 5, 8 33 , 5, 8 33
Major axis = 14 units
Minor axis = 8 units
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8- 4 Ellipses
2 2
3. Identify the center and foci and the lengths of
the major axis and minor axis for the ellipse.
5 81
16 49
x y
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8- 4 Ellipses
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2 22 5
4. Graph the ellipse: 116 4
x y
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8- 4 Ellipses
2 22 5
4. Graph the ellipse: 116 4
x y
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8- 4 Ellipses
2 22 5
4. Graph the ellipse: 116 4
x y
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8- 4 Ellipses
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2 24 3
5. Graph the ellipse: 19 36
x y
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8- 4 Ellipses
2 24 3
5. Graph the ellipse: 19 36
x y
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8- 4 Ellipses
2 24 3
5. Graph the ellipse: 19 36
x y
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8- 4 Ellipses
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6. Write an equation for the ellipse having:
endpoints of the major axis at 4,7 and 4, 1 ;
endpoints of the minor axis at 6,3 and 2,3 ;
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8- 4 Ellipses
6. Write an equation for the ellipse having:
endpoints of the major axis at 4,7 and 4, 1 ;
endpoints of the minor axis at 6,3 and 2,3 ;
2 24 3
14 16
x y
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8- 4 Ellipses
6. Write an equation for the ellipse having:
endpoints of the major axis at 4,7 and 4, 1 ;
endpoints of the minor axis at 6,3 and 2,3 ;
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8- 4 Ellipses
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7. Write an equation for the ellipse having:
center at 8, 3 ; minor axis of length 8 units;
foci at 8,9 and 8, 15 ;
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8- 4 Ellipses
7. Write an equation for the ellipse having:
center at 8, 3 ; minor axis of length 8 units;
foci at 8,9 and 8, 15 ;
2 28 3
116 128
x y
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8- 4 Ellipses
7. Write an equation for the ellipse having:
center at 8, 3 ; minor axis of length 8 units;
foci at 8,9 and 8, 15 ;
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8- 5 Hyperbolas
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2 2
1. Write an equation for the hyperbola in
standard form: 3 4 18 16 13 0x y x y
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8- 5 Hyperbolas
2 2
1. Write an equation for the hyperbola in
standard form: 3 4 18 16 13 0x y x y
2 23 2
18 6
x y
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8- 5 Hyperbolas
2 2
1. Write an equation for the hyperbola in
standard form: 3 4 18 16 13 0x y x y
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8- 5 Hyperbolas
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2 2
2. Identify the center, vertices, foci and the
equations of the asymptotes for the hyperbola:
6 1 1
16 25
x y
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8- 5 Hyperbolas
2 2
2. Identify the center, vertices, foci and the
equations of the asymptotes for the hyperbola:
6 1 1
16 25
x y
Center: 6,1
Vertices: 2,1 , 10,1
Foci: 6 41,1 , 6 41,1
5Asymptotes: 1 6
4y x
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8- 5 Hyperbolas
2 2
2. Identify the center, vertices, foci and the
equations of the asymptotes for the hyperbola:
6 1 1
16 25
x y
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8- 5 Hyperbolas
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2 2
3. Identify the center, vertices, foci and the
equations of the asymptotes for the hyperbola:
3 5 1
49 9
y x
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8- 5 Hyperbolas
2 2
3. Identify the center, vertices, foci and the
equations of the asymptotes for the hyperbola:
3 5 1
49 9
y x
Center: 5, 3
Vertices: 5,4 , 5, 10
Foci: 5, 3 58 , 5, 3 58
7Asymptotes: 3 5
3y x
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8- 5 Hyperbolas
2 2
3. Identify the center, vertices, foci and the
equations of the asymptotes for the hyperbola:
3 5 1
49 9
y x
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8- 5 Hyperbolas
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2 22 4
4. Graph the hyperbola: 125 4
y x
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8- 5 Hyperbolas
2 22 4
4. Graph the hyperbola: 125 4
y x
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8- 5 Hyperbolas
2 22 4
4. Graph the hyperbola: 125 4
y x
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8- 5 Hyperbolas
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2 26 3
5. Graph the hyperbola: 19 64
x y
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8- 5 Hyperbolas
2 26 3
5. Graph the hyperbola: 19 64
x y
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8- 5 Hyperbolas
2 26 3
5. Graph the hyperbola: 19 64
x y
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8- 5 Hyperbolas
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6. Write the equation of the hyperbola having:
vertices at 8,2 and 2,2 ; conjugate axis
of length 10 units
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8- 5 Hyperbolas
6. Write the equation of the hyperbola having:
vertices at 8,2 and 2,2 ; conjugate axis
of length 10 units
2 23 2
hyperbola; 125 25
x y
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8- 5 Hyperbolas
6. Write the equation of the hyperbola having:
vertices at 8,2 and 2,2 ; conjugate axis
of length 10 units
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8- 6 Identifying Conic Sections
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2 2
1. Identify the conic section, then write it in
standard form: 4 4 8 24 12 0x y x y
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8- 6 Identifying Conic Sections
2 2
1. Identify the conic section, then write it in
standard form: 4 4 8 24 12 0x y x y
2 2circle; 1 3 7x y
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8- 6 Identifying Conic Sections
2 2
1. Identify the conic section, then write it in
standard form: 4 4 8 24 12 0x y x y
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8- 6 Identifying Conic Sections
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2
2. Identify the conic section, then write it in
standard form: 3 6 2y x x
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8- 6 Identifying Conic Sections
2
2. Identify the conic section, then write it in
standard form: 3 6 2y x x
2parabola; 3 1 1y x
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8- 6 Identifying Conic Sections
2
2. Identify the conic section, then write it in
standard form: 3 6 2y x x
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8- 6 Identifying Conic Sections
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2 2
3. Identify the conic section, then write it in
standard form: 5 2 20 12 2 0x y x y
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8- 6 Identifying Conic Sections
2 2
3. Identify the conic section, then write it in
standard form: 5 2 20 12 2 0x y x y
2 22 3
ellipse; 18 20
x y
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8- 6 Identifying Conic Sections
2 2
3. Identify the conic section, then write it in
standard form: 5 2 20 12 2 0x y x y
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8- 6 Identifying Conic Sections
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2
4. Identify the conic section, then write it in
standard form: 2 8 1x y y
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8- 6 Identifying Conic Sections
2parabola; 2 2 9x y
2
4. Identify the conic section, then write it in
standard form: 2 8 1x y y
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8- 6 Identifying Conic Sections
2
4. Identify the conic section, then write it in
standard form: 2 8 1x y y
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8- 6 Identifying Conic Sections
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2 2
5. Identify the conic section, then write it in
standard form: 3 6 6 9x y x y
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8- 6 Identifying Conic Sections
2 2
5. Identify the conic section, then write it in
standard form: 3 6 6 9x y x y
2 23 1
hyperbola; 115 5
x y
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8- 6 Identifying Conic Sections
2 2
5. Identify the conic section, then write it in
standard form: 3 6 6 9x y x y