In this worksheet, we will practice finding the equation of a circle using its center and radius.

**Q4: **

Find the general form of the equation of circle , 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 centre 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 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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