Graphing Circles from Standard Equation Worksheets (High School Geometry)

📚 Topic Summary

The standard 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. Graphing a circle from its standard equation involves identifying the center and radius, plotting the center on the coordinate plane, and then drawing the circle using the radius as the distance from the center to any point on the circle.

Understanding this equation allows you to quickly visualize and sketch circles. The values of $h$ and $k$ determine the circle's position on the coordinate plane, while $r$ determines its size. Practice and familiarity with this equation are key to mastering circle graphing!

🔤 Part A: Vocabulary

Match the term with its definition:

1. Term: Radius
2. Term: Center
3. Term: Diameter
4. Term: Standard Equation of a Circle
5. Term: Coordinate Plane

1. Definition: The point from which all points on the circle are equidistant.
2. Definition: A plane containing a horizontal x-axis and a vertical y-axis.
3. Definition: The distance from the center of the circle to any point on the circle.
4. Definition: A straight line passing through the center of a circle and connecting two points on the circumference.
5. Definition: $(x - h)^2 + (y - k)^2 = r^2$

✍️ Part B: Fill in the Blanks

The standard equation of a circle is given by $(x - h)^2 + (y - k)^2 = r^2$, where the coordinates of the ______ are given by $(h, k)$, and the ______ of the circle is given by $r$. To graph the circle, first plot the ______ on the coordinate plane. Then, using the ______ as the distance, draw the circle.

🤔 Part C: Critical Thinking

Explain how changing the values of $h$, $k$, and $r$ in the standard equation affects the position and size of the circle on the graph.