# 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.

Q1:

Write, in the form , the equation of the circle of radius 10 and center .

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Q2:

Write the equation of the circle of center and diameter 10.

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Q3:

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

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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 . • A
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Q5:

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

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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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Q7:

What is the equation of the circle of radius 24 that lies in the third quadrant and is tangent to the two axes?

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Q8:

Find the point of intersection between the line with equation and the circle with center and radius 13.

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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 center 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. • A
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Q14:

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

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Q15:

Write, in the form , the equation of the circle of radius 10 and center .

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Q16:

Write, in the form , the equation of the circle of radius 9 and center .

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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. • A
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Q22:

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

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Q23:

In the figure below, we are given that and . Determine the equation of the circle at . • A
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Q24:

Find the center and radius of the circle .