Lesson Worksheet: Equation of a Circle Mathematics • 11th Grade

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In this worksheet, we will practice finding the equation of a circle using its center and a given point or the radius and vice versa.

Q1:

Write the equation of the circle of center and radius 9.

Q2:

In the figure below, find the equation of the circle.

Q3:

Give the general form of the equation of the circle of center and diameter 10.

Q4:

A circle has center and goes through the point . Find the equation of the circle.

Q5:

Find the equation of the circle represented by the given figure.

Q6:

Find the center and radius of the circle .

ACenter: , radius: 15
BCenter: , radius: 15
CCenter: , radius: 225
DCenter: , radius: 225
ECenter: , radius: 225

Q7:

Find the center and the radius of the circle .

ACenter: , radius: 10
BCenter: , radius: 10
CCenter: , radius: 10
DCenter: , radius: 100
ECenter: , radius: 100

Q8:

By completing the square, find the center and radius of the circle .

ACenter: , radius: 5
BCenter: , radius: 5
CCenter: , radius: 5
DCenter: , radius:
ECenter: , radius:

Q9:

The blueprint of a city is in a Cartesian coordinate system, where each unit represents 5 meters. Given that the circle represents one of the city’s squares, determine the area of the square to nearest square meter. Consider .

Q10:

Determine the general form of the equation of the circle that passes through the two points and , given that the circle’s center lies on the straight line .

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