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Lesson: Using Three Points to Find the Equation of a Circle

In this lesson, we will learn how to find the equation of a circle passing through three given points.

Sample Question Videos

06:27

Worksheet • 15 Questions • 1 Video

Q1:

Find the general equation of the circle through the origin that also passes through ( 1 2 , 0 ) and ( 0 , 1 6 ) .

  • A π‘₯ + 𝑦 βˆ’ 1 2 π‘₯ βˆ’ 1 6 𝑦 = 0 2 2
  • B π‘₯ + 𝑦 βˆ’ 2 4 π‘₯ βˆ’ 3 2 𝑦 + 3 0 0 = 0 2 2
  • C π‘₯ + 𝑦 + 1 2 π‘₯ + 1 6 𝑦 = 0 2 2
  • D π‘₯ + 𝑦 βˆ’ 6 π‘₯ βˆ’ 8 𝑦 = 0 2 2

Q2:

Find the general form of the equation of a circle that touches the π‘₯ -axis and passes through the two points ( βˆ’ 6 , βˆ’ 9 ) and ( 1 , βˆ’ 2 ) .

  • A π‘₯ + 𝑦 + 6 π‘₯ + 1 0 𝑦 + 9 = 0 2 2 , π‘₯ + 𝑦 βˆ’ 1 8 π‘₯ + 3 4 𝑦 + 8 1 = 0 2 2
  • B π‘₯ + 𝑦 + 6 π‘₯ + 1 0 𝑦 + 6 = 0 2 2 , π‘₯ + 𝑦 βˆ’ 1 8 π‘₯ + 3 4 𝑦 + 8 1 = 0 2 2
  • C π‘₯ + 𝑦 + 3 π‘₯ + 5 𝑦 + 9 = 0 2 2 , π‘₯ + 𝑦 βˆ’ 1 8 π‘₯ + 3 4 𝑦 + 8 1 = 0 2 2
  • D π‘₯ + 𝑦 + 6 π‘₯ + 1 0 𝑦 + 2 5 = 0 2 2 , π‘₯ + 𝑦 βˆ’ 1 8 π‘₯ + 3 4 𝑦 + 2 8 9 = 0 2 2

Q3:

Find the center of the circle through points 𝐴 ( 3 , 1 ) , 𝐡 ( 1 , 2 ) , and 𝐢 ( βˆ’ 1 , βˆ’ 2 ) .

  • A ( 1 , βˆ’ 0 . 5 )
  • B ( 1 . 5 , 0 . 5 )
  • C ( 0 , 1 . 5 )
  • D ( 2 , 0 )
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