Infinite Precalculus - Day 1 - Circles/Ellipses Worksheet

[Pages:6]Acc. Precalculus - Unit 2 - Conics

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Day 1 - Circles/Ellipses Worksheet

Date______________________ Period________

Use the information provided to write the standard form equation of each circle.

1) Center: (10, -5)

Radius: 5

2) Center: (11, 7)

Radius: 38

3) Center: (10, 0)

Radius: 8

4) Center: (-7, 3)

Radius: 6 2

5) Center: (14, -12) Point on Circle: (18, -14)

6) Center: (-14, 1) Point on Circle: (-13, 1)

7) Ends of a diameter: (4, 8) and (-8, 14)

8) Ends of a diameter: (9, 18) and (11, 0)

Identify the CENTER, VERTICES, CO-VERTICES, FOCI, LENGTH OF MAJOR AND MINOR AXIS and the ECCENTRICITY of each.

(x - 2)2 ( y + 10)2

9)

+

= 1

49

64

(x - 2)2 ( y - 7)2

10)

+

= 1

81

49

Worksheet by Kuta Software LLC

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( )17 2

x + 2

( y + 10)2

11)

+

= 1

144

81

Plot the CENTER and RADIUS of each. Then sketch the graph.

12) (x - 4)2 + ( y - 1)2 = 5

y 8

6

4

2

13) x2 + ( y - 3)2 = 9

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

14) x2 + y2 = 30

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

15) x2 + ( y + 2)2 = 4

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

Worksheet by Kuta Software LLC

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Sketch the graph. Plot the CENTER, FOCI, VERTICES and CO-VERTICES.

(x - 2)2 y2

16)

+ =1

4 49

y 8

6

4

2

(x - 1)2 ( y + 2)2

17)

+

= 1

36

9

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

x2 ( y + 2)2

18) +

= 1

30 10

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

Worksheet by Kuta Software LLC

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19) (x - 2)2 + ( y - 4)2 = 1

9

y 8

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

Worksheet by Kuta Software LLC

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Answers to Day 1 - Circles/Ellipses Worksheet

1) (x - 10)2 + ( y + 5)2 = 25

2) (x - 11)2 + ( y - 7)2 = 38

3) (x - 10)2 + y2 = 64

4) (x + 7)2 + ( y - 3)2 = 72

5) (x - 14)2 + ( y + 12)2 = 20

6) (x + 14)2 + ( y - 1)2 = 1

7) (x + 2)2 + ( y - 11)2 = 45

8) (x - 10)2 + ( y - 9)2 = 82

9) Center: (2, -10)

10) Center: (2, 7)

Vertices: (2, -2), (2, -18)

Vertices: (11, 7), (-7, 7)

Co-vertices: (9, -10), (-5, -10)

Co-vertices: (2, 14), (2, 0)

Foci: (2, -10 + 15), (2, -10 - 15)

Foci: (2 + 4 2, 7), (2 - 4 2, 7)

Major Axis: 16 units

Major Axis: 18 units

Minor Axis: 14 units

Minor Axis: 14 units

15

Eccentricity:

? 0.484

8

( ) 17

11) Center: - , -10 2

( ) ( ) 7

41

Vertices: , -10 , - , -10

2

2

( ) ( ) 17

17

Co-vertices: - , -1 , - , -19

2

2

( ) ( ) 6 7 - 17

-6 7 - 17

Foci:

, -10 ,

, -10

2

2

Major Axis: 24 units

Minor Axis: 18 units

42

Eccentricity:

? 0.629

9

12)

y 8

Center: (4, 1)

Radius: 5

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

7 Eccentricity: ? 0.661

4

13)

y 8

Center: (0, 3)

Radius: 3

6

4

2

14)

y 8

Center: (0, 0)

Radius: 30 6

4

2

15)

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

y 8

Center: (0, -2)

Radius: 2

6

4

2

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

16)

-8 -6 -4 -2 -2 -4 -6 -8

2 4 6 8x

y 8

Center: (2, 0) Vertices: (2, 7)

6

(2, -7)

4

Co-vertices: (4, 0)

2

(0, 0)

Foci: (2, 3 5)

-8 -6 -4 -2

2 4 6 8 x (2, -3 5)

-2

-4

-6

-8

Worksheet by Kuta Software LLC

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17) 19)

y 8

Center: (1, -2) Vertices: (7, -2)

6

(-5, -2)

4

Co-vertices: (1, 1)

2

(1, -5)

Foci: (1 + 3 3, -2)

-8 -6 -4 -2

2 4 6 8 x (1 - 3 3, -2)

-2

-4

-6

-8

y 8

Center: (2, 4) Vertices: (2, 7)

6

(2, 1)

4

Co-vertices: (3, 4)

2

(1, 4)

Foci: (2, 4 + 2 2)

-8 -6 -4 -2

2 4 6 8 x (2, 4 - 2 2)

-2

-4

-6

-8

18)

y 8

Center: (0, -2)

Vertices: ( 30, -2)

6

(- 30, -2)

4

Co-vertices: (0, -2 + 10)

2

(0, -2 - 10)

Foci: (2 5, -2)

-8 -6 -4 -2 2 4 6 8 x -2

(-2 5, -2)

-4

-6

-8

Worksheet by Kuta Software LLC

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