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 center at the point . Given that the circle intersects the -axis at points and , determine the area of .
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 circleβs 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 ?
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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