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Classify each conic section, write its equation in standard form, and sketch its graph. For parabolas,identify the vertex and focus. For circles, identify the center and radius. For ellipses and hyperbolasidentify the center, vertices, and foci.

17) 2 y2 + x 4 y + 1 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8

18) 25 x2 + y

2 100 x 125 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8

19) 4 x2 + 4 y

2 20 x 32 y + 81 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8

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20) 9 x2 + 4 y

2 54 x 8 y 59 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8

21) 9 x2 + 25 y

2 100 y 125 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8

22) y2 + x + 10 y + 26 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8

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Kuta Software - Infinite Algebra 2 Name___________________________________

Period____Date________________Classifying Conic Sections

Classify each conic section.

1) x2 + y

2 = 30

Circle

2) x2 + y

2 = 36

Circle

3) x

2

9 +

y2

16 = 1

Ellipse

4) x = y2

Parabola

5) x = ( y + 4 )2 2

Parabola6)

y2

25

x2

25 = 1

Hyperbola

7) y = ( x 1 )2 + 3

Parabola8) ( x 1 )2 + y

2

25 = 1

Ellipse

Classify each conic section and write its equation in standard form.

9) x2 + 10 x + y 21 = 0

Parabola

y = ( x 5 )2 4

10) 2 y2 + x 20 y 49 = 0

Parabola

x = 2 ( y + 5 )2 1

11) x2 + 2 x + y 1 = 0

Parabola

y = ( x + 1 )2 + 2

12) x2 + y

2 + 6 x 2 y + 9 = 0

Circle( x + 3 )2 + ( y 1 )2 = 1

13) x2 y

2 2 x 8 = 0

Hyperbola

( x 1 )2

9

y2

9 = 1

14) 3 x2 + 30 x + y + 79 = 0

Parabola

y = 3 ( x + 5 )2 4

15) 9 x2 + y

2 72 x 153 = 0

Hyperbola

y2

9 ( x + 4 )2 = 1

16) y2 + x + 8 y 17 = 0

Parabola

x = ( y 4 )2 + 1

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Classify each conic section, write its equation in standard form, and sketch its graph. For parabolas,identify the vertex and focus. For circles, identify the center and radius. For ellipses and hyperbolasidentify the center, vertices, and foci.

17) 2 y2 + x 4 y + 1 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8 Parabola x = 2 ( y + 1 )2 3Vertex: (3 , 1 )

Focus: ( 238 , 1 )

18) 25 x2 + y

2 100 x 125 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8 Hyperbola

y2

25 ( x + 2 )2 = 1

Center: (2 , 0 )Vertices: (2 , 5 ), (2 , 5 )Foci: (2 , 26 ), (2 , 26 )

19) 4 x2 + 4 y

2 20 x 32 y + 81 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8 Circle

( x 52 )2

+ ( y 4 )2 = 2

Center: (52 , 4)Radius: 2

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20) 9 x2 + 4 y

2 54 x 8 y 59 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8 Ellipse( x 3 )2

16 +

( y 1 )2

36 = 1

Center: (3 , 1 )Vertices: (3 , 7 ), (3 , 5 )Foci: (3 , 1 + 2 5 ), (3 , 1 2 5 )

21) 9 x2 + 25 y

2 100 y 125 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8 Hyperbola( y 2 )2

9 x

2

25 = 1

Center: (0 , 2 )Vertices: (0 , 5 ), (0 , 1 )Foci: (0 , 2 + 34 ), (0 , 2 34 )

22) y2 + x + 10 y + 26 = 0

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8 Parabola x = ( y + 5 )2 1Vertex: (1 , 5 )

Focus: ( 54 , 5 )

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