Test Questions for Circles: Mastering the Standard Form Equation and Graphing

📚 Quick Study Guide

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• The standard form equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius.
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• The center of the circle, $(h, k)$, represents the coordinates of the circle's central point on the Cartesian plane.
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• The radius, $r$, is the distance from the center of the circle to any point on its circumference.
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• To graph a circle, first identify the center $(h, k)$ and the radius $r$ from the standard form equation.
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• Plot the center on the coordinate plane.
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• From the center, count $r$ units up, down, left, and right, and plot these four points.
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• Sketch the circle by connecting these points with a smooth curve.

Practice Quiz

1. What are the coordinates of the center of the circle with the equation $(x - 3)^2 + (y + 2)^2 = 16$?
1. (3, 2)
2. (-3, -2)
3. (3, -2)
4. (-3, 2)
2. What is the radius of the circle with the equation $(x + 1)^2 + (y - 5)^2 = 9$?
1. 3
2. 9
3. 81
4. 1
3. The center of a circle is at (0, 0), and its radius is 5. What is the equation of the circle in standard form?
1. $x^2 + y^2 = 5$
2. $x^2 + y^2 = 10$
3. $x^2 + y^2 = 25$
4. $x^2 + y^2 = 1$
4. Which of the following points lies on the circle with equation $(x - 2)^2 + (y + 1)^2 = 4$?
1. (2, 1)
2. (0, -1)
3. (2, -2)
4. (4, 1)
5. What is the equation of a circle with center (-2, 3) and radius 4?
1. $(x - 2)^2 + (y + 3)^2 = 16$
2. $(x + 2)^2 + (y - 3)^2 = 16$
3. $(x - 2)^2 + (y + 3)^2 = 4$
4. $(x + 2)^2 + (y - 3)^2 = 4$
6. The equation of a circle is $(x - 1)^2 + (y - 2)^2 = 25$. What is the diameter of the circle?
1. 5
2. 10
3. 25
4. 50
7. Which equation represents a circle with a center on the y-axis?
1. $(x - 3)^2 + y^2 = 9$
2. $x^2 + (y - 2)^2 = 4$
3. $(x - 1)^2 + (y - 1)^2 = 1$
4. $(x + 2)^2 + (y + 3)^2 = 16$