Lesson: Equation of a Circle Passing through Three Points

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: Equation of a Circle Passing through Three Points • 15 Questions • 1 Video

Q1:

Find the equation of the circle that passes through the points 𝐴 ( − 4 , − 3 ) , 𝐵 ( − 3 , − 4 ) , and 𝐶 ( − 2 , − 3 ) .

Q2:

Determine the general equation of the shown circle 𝑀 passing through the origin point and the two points 𝐴 ( 8 , 0 ) and 𝐵 ( 0 , − 1 0 ) .

Q3:

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

Q4:

Find the general form of the equation of a circle that touches the 𝑥 -axis and passes through the two points ( − 6 , − 9 ) and ( 1 , − 2 ) .

Q5:

Find the centre of the circle through points 𝐴 ( 3 , 1 ) , 𝐵 ( 1 , 2 ) , and 𝐶 ( − 1 , − 2 ) .

Q6:

The points 𝐴 ( 1 , − 1 ) , 𝐵 ( − 1 , 5 ) , 𝐶 ( 1 7 , 1 1 ) , and 𝐷 ( 1 9 , 5 ) form a rectangle. What is the equation of the circle that contains all four points?

Q7:

The coordinates for three of a group of aerialists in a circular formation are 𝐺 ( 2 3 , − 9 ) , 𝐻 ( 1 2 , 2 ) , and 𝐽 ( 1 2 , − 2 0 ) . If each unit represents 1 foot, determine the diameter of their circular formation.

Q8:

Find the equation of the circle that passes through the points 𝐴 ( 2 , − 1 ) , 𝐵 ( 5 , 2 ) , and 𝐶 ( 2 , 5 ) .

Q9:

Find the equation of the circle that passes through the points 𝐴 ( 6 , 1 ) , 𝐵 ( − 3 , 1 0 ) , and 𝐶 ( − 1 2 , 1 ) .

Q10:

Find the equation of the circle that passes through the points 𝐴 ( 8 , 7 ) , 𝐵 ( 1 , 8 ) , and 𝐶 ( 0 , 1 ) .

Q11:

Find the equation of the circle that passes through the points 𝐴 ( 1 , − 6 ) , 𝐵 ( 0 , 1 ) , and 𝐶 ( − 7 , 0 ) .

Q12:

Find the equation of the circle that passes through the points 𝐴 ( 1 2 , − 2 ) , 𝐵 ( 4 , 6 ) , and 𝐶 ( − 4 , − 2 ) .

Q13:

Find the equation of the circle that passes through the points 𝐴 ( 5 , 4 ) , 𝐵 ( − 2 , 5 ) , and 𝐶 ( − 3 , − 2 ) .

Q14:

Find the equation of the circle that passes through the points 𝐴 ( 2 , 3 ) , 𝐵 ( − 3 , 8 ) , and 𝐶 ( − 8 , 3 ) .

Q15:

Find the equation of the circle that passes through the points 𝐴 ( − 4 , − 2 ) , 𝐵 ( − 6 , − 4 ) , and 𝐶 ( − 4 , − 6 ) .
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