# Worksheet: Equation of a Circle Passing through Three Noncollinear Points

In this worksheet, we will practice finding the equation of a circle passing through three noncollinear points that form a right triangle.

Q1:

Find the equation of the circle that passes through the points , , and .

• A
• B
• C
• D

Q2:

Determine the general equation of the shown circle passing through the origin point and the two points and . • A
• B
• C
• D

Q3:

Find the general equation of the circle through the origin that also passes through and .

• A
• B
• C
• D

Q4:

Find the general form of the equation of a circle that touches the -axis and passes through the two points and .

• A,
• B,
• C,
• D,

Q5:

Find the centre of the circle through points , , and .

• A
• B
• C
• D

Q6:

The points , , , and form a rectangle. What is the equation of the circle that contains all four points?

• A
• B
• C
• D

Q7:

The coordinates for three of a group of aerialists in a circular formation are , , and . 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 , , and .

• A
• B
• C
• D

Q9:

Find the equation of the circle that passes through the points , , and .

• A
• B
• C
• D

Q10:

Find the equation of the circle that passes through the points , , and .

• A
• B
• C
• D

Q11:

Find the equation of the circle that passes through the points , , and .

• A
• B
• C
• D

Q12:

Find the equation of the circle that passes through the points , , and .

• A
• B
• C
• D

Q13:

Find the equation of the circle that passes through the points , , and .

• A
• B
• C
• D

Q14:

Find the equation of the circle that passes through the points , , and .

• A
• B
• C
• D

Q15:

Find the equation of the circle that passes through the points , , and .

• A
• B
• C
• D

Q16:

How many circles can pass through three vertices of a parallelogram?

Q17:

Find the general equation of the circle if the circle touches the -axis at and intersects the -axis at and . • A
• B
• C
• D