# Worksheet: Equation of a Circle

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.

**Q4: **

Find the general form of the equation of the circle with center , given that it touches the two coordinate axes at and and that .

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**Q6: **

Determine the equation of a circle with radius , given that it touches the -axis at the point , and its center lies in the third quadrant.

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**Q9: **

Let us consider a circle of radius 4 and center .

Write the equation of the circle.

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The circle is dilated by a factor of 2. The center of dilation is the center of the circle. Write the equation of the circle.

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**Q10: **

Let us consider a circle of radius 6 and center .

Write the equation of the circle.

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The circle is dilated by a factor of . The center of dilation is the center of the circle. Write the equation of the circle.

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**Q11: **

A circle is tangent to the -axis at and cuts a chord of length on the negative-axis. What is the equation of the circle?

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**Q12: **

A circle of radius 15 length units has its centre at the point . Given that the circle intersects the -axis at points and , determine the area of .

**Q13: **

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

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**Q14: **

Given and , find the equation of the circle with diameter .

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**Q17: **

Let us consider a circle of radius 5 and center .

Write the equation of the circle.

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The circle undergoes a dilation by a scale factor of three, centered at , and then a translation six units to the left and three units up. Write the equation of the circle.

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**Q18: **

Determine the equation of a circle with a diameter of 14 feet whose center was translated 15 feet left and 14 feet up from the origin.

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**Q19: **

Find the equation of a circle which has the radius as the circle , and two of whose diameters lie on lines and .

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**Q20: **

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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**Q21: **

Find the general form of the equation of the circle if the straight line of equation passes through the center of the circle and the origin.

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**Q22: **

A circle has circumference and intersects the -axis at points and . What are the possible equations for ?

- A ,
- B ,
- C ,
- D ,

**Q23: **

In the figure below, we are given that and . Determine the equation of the circle at .

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**Q24: **

Find the center and radius of the circle .

- Acenter: , radius: 10
- Bcenter: , radius: 100
- Ccenter: , radius: 100
- Dcenter: , radius: 100
- Ecenter: , radius: 10

**Q25: **

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: