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Worksheet: The Center and Radius of a Circle

Q1:

Find the center and radius of the circle π‘₯ + 6 π‘₯ + 𝑦 + 1 8 𝑦 + 2 6 = 0 2 2 .

  • A center: ( βˆ’ 3 , 9 ) , radius: 8
  • B center: ( βˆ’ 3 , βˆ’ 9 ) , radius: 64
  • C center: ( 3 , 9 ) , radius: 64
  • D center: ( βˆ’ 3 , βˆ’ 9 ) , radius: 8
  • Ecenter: ( βˆ’ 9 , βˆ’ 3 ) , radius: 64

Q2:

Find the center and radius of the circle π‘₯ + 3 π‘₯ + 𝑦 + 8 3 𝑦 βˆ’ 3 4 5 5 3 6 = 0   .

  • A center: ο€Ό 3 2 , 4 3  , radius: 10
  • B center: ο€Ό 3 2 , βˆ’ 4 3  , radius: 100
  • C center: ο€Ό βˆ’ 3 2 , 4 3  , radius: 100
  • D center: ο€Ό βˆ’ 3 2 , βˆ’ 4 3  , radius: 10
  • Ecenter: ο€Ό βˆ’ 4 3 , 3 2  , radius: 100

Q3:

By completing the square, find the center and radius of the circle π‘₯ + 6 π‘₯ + 𝑦 βˆ’ 4 𝑦 + 8 = 0 2 2 .

  • A center: ( 2 , βˆ’ 3 ) , radius: √ 5
  • B center: ( 3 , βˆ’ 2 ) , radius: 5
  • C center: ( 2 , βˆ’ 3 ) , radius: 5
  • D center: ( βˆ’ 3 , 2 ) , radius: √ 5
  • E center: ( βˆ’ 3 , 2 ) , radius: 5

Q4:

Find the center and radius of the circle π‘₯ + 7 π‘₯ + 𝑦 βˆ’ 4 . 6 𝑦 βˆ’ 7 . 4 6 = 0 2 2 .

  • A center: ( 3 . 5 , 2 . 3 ) , radius: 5
  • B center: ( 3 . 5 , βˆ’ 2 . 3 ) , radius: 25
  • C center: ( βˆ’ 3 . 5 , βˆ’ 2 . 3 ) , radius: 25
  • D center: ( βˆ’ 3 . 5 , 2 . 3 ) , radius: 5
  • Ecenter: ( βˆ’ 3 . 5 , 2 . 3 ) , radius: 25

Q5:

The line 𝑦 = βˆ’ 7 touches the circle of center ( 7 , 9 ) . What is the radius of the circle?

  • A7 length units
  • B16 length units
  • C14 length units
  • D32 length units

Q6:

By completing the square, find the center and radius of the circle π‘₯ + 1 6 π‘₯ + 𝑦 + 1 2 𝑦 + 9 7 = 0 2 2 .

  • A center: ( 8 , 6 ) , radius: √ 3
  • B center: ( 8 , βˆ’ 6 ) , radius: 3
  • C center: ( βˆ’ 8 , 6 ) , radius: 3
  • D center: ( βˆ’ 8 , βˆ’ 6 ) , radius: √ 3
  • Ecenter: ( βˆ’ 8 , βˆ’ 6 ) , radius: 3

Q7:

Which of the following points lies on the circle of center ( 0 , 0 ) and radius 10?

  • A ( βˆ’ 1 2 , 6 )
  • B ( βˆ’ 1 0 , 3 )
  • C ( βˆ’ 8 , 4 )
  • D ( βˆ’ 8 , 6 )
  • E ( βˆ’ 7 , 6 )

Q8:

Find the center and radius of the circle π‘₯ + 6 π‘₯ + 𝑦 βˆ’ 9 𝑦 + 8 1 4 = 0 2 2 .

  • A center: ο€Ό 3 , βˆ’ 9 2  , radius: 3
  • B center: ο€Ό βˆ’ 3 , 9 2  , radius: 9
  • C center: ο€Ό βˆ’ 3 , βˆ’ 9 2  , radius: 9
  • D center: ο€Ό βˆ’ 3 , 9 2  , radius: 3
  • Ecenter: ο€Ό 9 2 , βˆ’ 3  , radius: 3

Q9:

Find the center and radius of the circle ( π‘₯ βˆ’ 2 ) + ( 𝑦 + 8 ) βˆ’ 1 0 0 = 0 2 2 .

  • A center: ( 2 , βˆ’ 8 ) , radius: 100
  • B center: ( βˆ’ 2 , 8 ) , radius: 10
  • C center: ( βˆ’ 8 , 2 ) , radius: 100
  • D center: ( 2 , βˆ’ 8 ) , radius: 10
  • Ecenter: ( βˆ’ 8 , 2 ) , radius: 10

Q10:

Find the center and radius of the circle ( π‘₯ + 4 ) + ( 𝑦 βˆ’ 2 ) = 2 2 5 2 2 .

  • A center: ( βˆ’ 2 , 4 ) , radius: 225
  • B center: ( 4 , βˆ’ 2 ) , radius: 225
  • C center: ( 2 , βˆ’ 4 ) , radius: 15
  • D center: ( βˆ’ 4 , 2 ) , radius: 15
  • Ecenter: ( βˆ’ 4 , 2 ) , radius: 225