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