Worksheet: Intersections of Circles and Lines

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

Q1:

Consider the circle (𝑥5)+(𝑦+2)=25. Is the line 𝑦3=0 tangent to, intersecting, or disjoint from the circle?

  • Adisjoint from the circle
  • Btangent to the circle
  • Cintersecting the circle

Q2:

Which of the following points lies on the circle 𝑦+(𝑥+6)=144?

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

Q3:

The line 4𝑦3𝑥2=0 meets the circle 𝑥+𝑦+6𝑥+4𝑦=0 in points 𝐴 and 𝐵. Determine the distance between the center of the circle and 𝐴𝐵.

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(3, 11)
  • C ( 2 , 1 )
  • D(0, 2)
  • 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 ( 4 , 1 )
  • B ( 6 , 7 )
  • C ( 2 , 5 )
  • D ( 5 , 2 )
  • E ( 2 , 5 )

Q6:

Which of the following points lies on the circle (𝑥+1)+(𝑦2)=4?

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

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