Worksheet: Intersections of Circles and Lines

In this worksheet, we will practice finding points of intersections between circles and lines.

Q1:

Consider the circle ( 𝑥 5 ) + ( 𝑦 + 2 ) = 2 5 2 2 . Is the line 𝑦 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 points lies on the circle 𝑦 + ( 𝑥 + 6 ) = 1 4 4 2 2 ?

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

Q3:

The line 4 𝑦 3 𝑥 2 = 0 meets circle 𝑥 + 𝑦 + 6 𝑥 + 4 𝑦 = 0 in points 𝐴 and 𝐵 . How far is the centre of the circle from 𝐴 𝐵 .

Q4:

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

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

Q5:

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

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

Q6:

Which of the following points lies on the circle ( 𝑥 + 1 ) + ( 𝑦 2 ) = 4 2 2 ?

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

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