Equation of a Circle Worksheet
Practice identifying, writing, and graphing equations of circles in standard and general forms.
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Equation of a Circle
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. What is the standard form of the equation of a circle with center (h, k) and radius r?
(x + h)² + (y + k)² = r²
(x - h)² + (y - k)² = r²
x² + y² = r²
(x - r)² + (y - r)² = h² + k²
2. A circle has its center at the origin (0,0) and a radius of 5. Which of the following is its equation?
x² + y² = 5
(x - 0)² + (y - 0)² = 5
x² + y² = 25
(x - 5)² + (y - 5)² = 0
3. The of a circle is the distance from its center to any point on the circle.
4. The equation (x + 3)² + (y - 1)² = 49 represents a circle with center at and a radius of .
5. Write the standard form of the equation of a circle with center (-2, 5) and a radius of 3.
6. Find the center and radius of the circle given by the equation (x - 7)² + y² = 16.
7. Graph the circle defined by the equation x² + y² = 9.
8. Graph the circle defined by the equation (x + 1)² + (y - 2)² = 4.
9. Convert the general form of the circle equation x² + y² - 6x + 4y - 12 = 0 into standard form. Then, identify the center and radius of the circle.