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Worksheet: Intersections of Circles and Lines

Q1:

Consider the circle ( π‘₯ βˆ’ 5 ) + ( 𝑦 + 2 ) = 2 5 2 2 . Is the line 𝑦 βˆ’ 3 = 0 tangent to, intersecting, or disjoint from the circle?

  • Adisjoint from the circle
  • Bintersecting the circle
  • Ctangent to the circle

Q2:

Which of the following is a point of intersection between Circles 𝐴 and 𝐡 where Circle 𝐴 has radius 10 and center (9,3) and Circle 𝐡 has radius 5 and center (0,7)?

  • A(0, 7)
  • B(0, 2)
  • C ( 2 , βˆ’ 1 )
  • D(3, 11)
  • E(4, 12)

Q3:

Which of the following points lies on the circle 𝑦 + ( π‘₯ + 6 ) = 1 4 4 2 2 ?

  • A ( 1 1 , 1 2 7 )
  • B ( βˆ’ 6 , 0 )
  • C ( 6 , 1 2 )
  • D ( 6 , 0 )

Q4:

Which of the following points lies on the circle ( π‘₯ + 1 ) + ( 𝑦 βˆ’ 2 ) = 4 2 2 ?

  • A ( 1 2 , βˆ’ 7 )
  • B ( βˆ’ 1 , 2 )
  • C ( 1 , 4 )
  • D ( βˆ’ 1 , 4 )

Q5:

Which of the following is a point of intersection between Circles A and B where Circle A has radius 13 and center ( βˆ’ 7 , 7 ) and Circle B has radius 5 and center ( 9 , βˆ’ 1 ) ?

  • A ( βˆ’ 2 , 5 )
  • B ( 4 , βˆ’ 1 )
  • C ( 2 , 5 )
  • D ( 5 , 2 )
  • E ( 6 , 7 )

Q6:

The line βˆ’ 4 𝑦 βˆ’ 3 π‘₯ βˆ’ 2 = 0 meets circle π‘₯ + 𝑦 + 6 π‘₯ + 4 𝑦 = 0 2 2 in points 𝐴 and 𝐡 . How far is the center of the circle from 𝐴 𝐡 .

  • A5
  • B15
  • C9
  • D3