Worksheet: The Center and Radius of a Circle

In this worksheet, we will practice finding the center and radius of a circle from its equation.

Q1:

Find the centre and radius of the circle ( 𝑥 2 ) + ( 𝑦 + 8 ) 1 0 0 = 0 2 2 .

  • A centre: ( 2 , 8 ) , radius: 100
  • B centre: ( 2 , 8 ) , radius: 10
  • C centre: ( 8 , 2 ) , radius: 100
  • D centre: ( 2 , 8 ) , radius: 10
  • Ecentre: ( 8 , 2 ) , radius: 10

Q2:

Find the centre and radius of the circle 𝑥 + 6 𝑥 + 𝑦 + 1 8 𝑦 + 2 6 = 0 2 2 .

  • A centre: ( 3 , 9 ) , radius: 8
  • B centre: ( 3 , 9 ) , radius: 64
  • C centre: ( 3 , 9 ) , radius: 64
  • D centre: ( 3 , 9 ) , radius: 8
  • Ecentre: ( 9 , 3 ) , radius: 64

Q3:

Find the center and radius of the circle 𝑥 + 𝑦 + 1 0 𝑥 1 8 𝑦 + 4 2 = 0 .

  • A ( 5 , 9 ) 4 2 ,
  • B ( 1 0 , 1 8 ) 4 2 ,
  • C ( 1 0 , 1 8 ) 8 ,
  • D ( 5 , 9 ) 8 ,

Q4:

Find the center and radius of the circle ( 𝑥 + 4 ) + ( 𝑦 2 ) = 2 2 5 .

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

Q5:

By completing the square, find the centre and radius of the circle 𝑥 + 6 𝑥 + 𝑦 4 𝑦 + 8 = 0 2 2 .

  • A centre: ( 2 , 3 ) , radius: 5
  • B centre: ( 3 , 2 ) , radius: 5
  • C centre: ( 2 , 3 ) , radius: 5
  • D centre: ( 3 , 2 ) , radius: 5
  • E centre: ( 3 , 2 ) , radius: 5

Q6:

By completing the square, find the centre and radius of the circle 𝑥 + 1 6 𝑥 + 𝑦 + 1 2 𝑦 + 9 7 = 0 2 2 .

  • A centre: ( 8 , 6 ) , radius: 3
  • B centre: ( 8 , 6 ) , radius: 3
  • C centre: ( 8 , 6 ) , radius: 3
  • D centre: ( 8 , 6 ) , radius: 3
  • Ecentre: ( 8 , 6 ) , radius: 3

Q7:

Find the centre and radius of the circle 𝑥 + 6 𝑥 + 𝑦 9 𝑦 + 8 1 4 = 0 2 2 .

  • A centre: 3 , 9 2 , radius: 3
  • B centre: 3 , 9 2 , radius: 9
  • C centre: 3 , 9 2 , radius: 9
  • D centre: 3 , 9 2 , radius: 3
  • Ecentre: 9 2 , 3 , radius: 3

Q8:

Find the centre and radius of the circle 𝑥 + 7 𝑥 + 𝑦 4 . 6 𝑦 7 . 4 6 = 0 2 2 .

  • A centre: ( 3 . 5 , 2 . 3 ) , radius: 5
  • B centre: ( 3 . 5 , 2 . 3 ) , radius: 25
  • C centre: ( 3 . 5 , 2 . 3 ) , radius: 25
  • D centre: ( 3 . 5 , 2 . 3 ) , radius: 5
  • Ecentre: ( 3 . 5 , 2 . 3 ) , radius: 25

Q9:

Find the center and radius of the circle 𝑥 + 3 𝑥 + 𝑦 + 8 3 𝑦 3 4 5 5 3 6 = 0 .

  • A center: 3 2 , 4 3 , radius: 10
  • B center: 3 2 , 4 3 , radius: 100
  • C center: 3 2 , 4 3 , radius: 100
  • D center: 3 2 , 4 3 , radius: 10
  • Ecenter: 4 3 , 3 2 , radius: 100

Q10:

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

Q11:

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

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

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