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Algebra
Conic Section Review
Review Conic Section
1. Why is this section called conic section?
2. Review equation of each conic section
A summary of circles, ellipses, parabolas and hyperbolas
http://britton.disted.camosun.bc.ca/jbconics.htm
Each shape comes from slicing a cone.
Vertex=
Directrix:
Open :
Information about _____________________
Fill in the blank below and complete the following examples.
Focus:
538
1 2 xy
Vertex=
Directrix:
Open :
Information about _____________________
Fill in the blank below and complete the following examples.
Focus:
538
1 2 xy
Information about _____________________
Fill in the blank below and complete the following examples.
24 2 yx
Vertex=
Directrix:
Open :
Focus:
Information about _____________________
Fill in the blank below and complete the following examples.
24 2 yx
Vertex=
Directrix:
Open :
Focus:
Center:
Vertices:
Co-Vertices
Foci:
Information about equation of _____________________
Fill in the blank and complete the following examples.
1
36
7
9
4 22
yx
Center:
Vertices:
Co-Vertices
Foci:
Information about equation of _____________________
Fill in the blank and complete the following examples.
1
36
7
9
4 22
yx
Information about equation of _____________________
Fill in the blank and complete the following examples.
2 25 2
149 37
x y
Center:
Vertices:
Co-Vertices
Foci:
Information about equation of _____________________
Fill in the blank and complete the following examples.
2 25 2
149 37
x y
Center:
Vertices:
Co-Vertices:
Foci:
Center:
Radius:
Complete the problem by finding the missing parts.
49235.7 22 yx
Center:
Radius:
Complete the problem by finding the missing parts.
49235.7 22 yx
Center:
Vertices:
Foci:
Information for ____________
Fill in the blank and then complete the examples.
1
25
5
12
1 22
yx
Center:
Vertices:
Foci:
Information for ____________
Fill in the blank and then complete the examples.
1
25
5
12
1 22
yx
Center:
Vertices:
Foci:
Information for ____________
Fill in the blank and then complete the examples.
2 21 2
1100 64
y x
Center:
Vertices:
Foci:
Information for ____________
Fill in the blank and then complete the examples.
2 21 2
1100 64
y x
1. What is the graph of 4x2 = y2 + 8y + 32 ?
A. Circle B. Parabola C. Ellipse D. Hyperbola
2. What is the graph of 5x2 + 10x + 5y2 = 9?
A. Circle B. Parabola C. Ellipse D. Hyperbola
3. What is the graph of 4x2 = y – 24x + 35?
A. Circle B. Parabola C. Ellipse D. Hyperbola
4. What is the graph of 9x2 + 4y2 +36x- 24y + 36=0 ?
A. Circle B. Parabola C. Ellipse D. Hyperbola
5. Write the equation of the parabola whose vertex is at (4,-3) and whose focus is at (4,8)?
3444
1 2 xy
5. Write the equation of the parabola whose vertex is at (4,-3) and whose focus is at (4,8)?
3444
1 2 xy
6. Which of the following is an equation for the circle whose center is at (-3,6) and the radius is 4?
A.(x – 3)2 + (y – 6)2 = 8
B. (x + 3)2 + (y + 6)2 = 16
C. (x + 3)2 – (y – 6)2 = 24
D. (x + 3)2 + (y – 6)2 = 16
E. (x – 3)2 – (y – 6)2 = 4
D
7. Which of the following is an equation of the ellipse with foci at (2,4) and (-6,4) and vertices at (-8,4) and (4,4)?
1
20
4
36
2.
136
4
20
2.
120
4
36
2.
120
2
36
4.
136
2
20
4.
22
22
22
22
22
yxE
yxD
yxC
yxB
yxA C
8. What is the standard form of the hyperbola with foci at (0,5), (0,-5) and Vertices at (0,2), (0,-2)?
1214
22
xy
8. What is the standard form of the hyperbola with foci at (0,5), (0,-5) and Vertices at (0,2), (0,-2)?
1214
22
xy
9. What are the foci of the ellipse 17x2 +8y2 =136?
(0,3), (0-3)
9. What are the foci of the ellipse 17x2 +8y2 =136?
(0,3), (0-3)
10. What is the directrix of the parabola with equation x2 =-28y ?
A. x = 28B. y= -7C. y = 7D. y= -28E. x= 7
C
A circle has a diameter with endpoints of (8, –1) and (0, –1).
Find the radius.
Write the equation for the circle in standard form.
A circle has a diameter with endpoints of (8, –1) and (0, –1).
Find the radius.
Write the equation for the circle in standard form.
11. Name the conic section first. Then, graph it.
x + 10 = -2y2 – 12y
11. Name the conic section first. Then, graph it.
x + 10 = -2y2 – 12y
12. Name the conic section first. Then, graph it.
x2 +y2 +8y +4x-5=0
12. Name the conic section first. Then, graph it.
x2 +y2 +8y +4x-5=0
13. Name the conic section first. Then, graph it.
x2 + 4y2 + 10x + 24y + 45=0
13. Name the conic section first. Then, graph it.
x2 + 4y2 + 10x + 24y + 45=0
14. Name the conic section first. Then, graph it.
4y2 - 25x2 = 100
14. Name the conic section first. Then, graph it.
4y2 - 25x2 = 100
15. Name the conic section first. Then, graph it.
36y2 -4x2 + 216y -40x + 80=0
15. Name the conic section first. Then, graph it.
36y2 -4x2 + 216y -40x + 80=0