Conics

1

2

34

78

6

5

10

1211

9

1615

14

13

This presentation was written by Rebecca HoffmanRetrieved from McEachern High School

1

Name the vertex and the distance from the vertex to the focus of the equation (y+4)2 = -16(x-1)

Question:

Answer:

Vertex: (1, -4)

p = -4

2

Write the equation in standard form

18x2 + 12y2 - 144x - 48y + 120 = 0

Question:

Answer:

( )x y

4

12

2

181

2 2b g

3

Write the equation in standard form

9x2 - 4y2 - 54x - 40y - 55 = 0

Question:

Answer:

x y

3

4

5

91

2 2b g b g

4

Determine the equation of the circle with center

(-4,7) and a solution point (1,2).

Question:

Answer:

2 2( 4) ( 7) 50x y

5

Write in standard form:

x2 + 4x - y + 8 = 0

Question:

Answer:

(x + 2)2 = y - 4

6

Graph: x y

4

16

6

91

2 2b g b gQuestion:

Answer:

Center: (4, -6)

Vertices: (8, -6) (0, -6)

Pseudovertices: (4, -3) (4, -9)

Foci: (6.6, -6) (1.4, -6)

7

Graph: y x

1

4

3

251

2 2b g b gQuestion:

Answer:Center: (3,1)

Vertices: (3,3) (3,-1)

Foci: (3, 6.4) (3, -4.4)

Pseudovertices: (8,1) (-2,1)

8

The following equations will graph

which type of conic section?

2 5 19 02x x y y y x x2 29 7 3 52

A)

B)

C) x x y y2 22 24 41 3

parabola

hyperbola

ellipse

Question:

Answer:

9

Graph: (x-2)2 = 8(y-3)Question:

Answer:

Vertex: (2, 3)

Focus: (2, 5)

Directrix: y = 1

Semilatus = 4

10Write the equation from the graphQuestion:

Answer:x y2 2

49

5

251

b g

11Question:

Answer:

Write the equation of the hyperbola whose

covertices are 6 units apart and vertices are (3,4) and (3,0)

y x

2

4

3

91

2 2b g b g Center: (3, 2)

a = 2

b = 3

12

Determine the equation of the conic section

represented by: 4y2 - 8y + 4x2 - 56x + 49 = 0

Question:

Answer:

2 2 1517 1

4x y

13Write the equation from the graphQuestion:

Answer:(y-2)2=4(x+4)

(-4, 2)

14

Write the equation of the ellipse with

vertical major axis 20 units long, and center at (3,0) and a foci at (3,7)

Question:

Answer:

y x2 2

100

3

511

b gh = 3 k = 0

a = 10

c = 7

b 51

15

Write the equation of the hyperbola

and foci at (0, 9) and (0,-1) and a co-vertex at (-3,4)

Question:

Answer:

y x

4

16 91

2 2b g Center: (0, 4)

a = 4

b = 3

c = 5

16

Question:

Answer:

Write the equation of the conic with center at (3, 1),

vertical major axis 12 units long, and a focus at (3,3).

1

32

3

36

1 22

xy

Final Jeopardy

Identify the conic section

Write the equation in standard form

Graph the equation

Question:

x2 - 6y - 8x + 16 = 0

Final JeopardyQuestion: x2 - 6y - 8x + 16 = 0

Answer: parabola (x - 4)2 = 6yVertex: (4,0) focus: (4, 1.5)

Directrix: y = -1.5 Axis: x = 4

p=1.5