algebra conic section review. review conic section 1. why is this section called conic section? 2....

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