What is how to graph a circle?

Graphing a Circle

To graph a circle, you need two key pieces of information:

1. The Center: This is the point (h, k) that represents the center of the circle. This is the starting point for your graph. See also the concept of Coordinate%20Plane.

2. The Radius: This is the distance, 'r', from the center of the circle to any point on the circle. It determines the size of the circle. See also the concept of Distance.

The standard form equation of a circle is:

(x - h)^2 + (y - k)^2 = r^2

Steps to Graph a Circle:

1. Identify the Center (h, k) and Radius (r): From the equation, determine the values of h, k, and r. Remember that the equation has (x - h) and (y - k), so if you see (x + 3), then h = -3. Find the Square%20Root of the number on the right side of the equation to obtain r.

2. Plot the Center: Plot the point (h, k) on the coordinate plane.

3. Plot Points Based on the Radius: From the center, move 'r' units in each of the four cardinal directions (up, down, left, and right). This will give you four points on the circle.

4. Sketch the Circle: Connect the four points you plotted (and any additional points if needed) to form a smooth circle. Aim for a shape that is as circular as possible.

Example:

Let's say you have the equation: (x - 2)^2 + (y + 1)^2 = 9

• Center: (h, k) = (2, -1)
• Radius: r = √9 = 3

1. Plot the point (2, -1).
2. From (2, -1), move 3 units up to (2, 2), 3 units down to (2, -4), 3 units right to (5, -1), and 3 units left to (-1, -1).
3. Sketch a circle connecting these four points.

Important Considerations:

• If the equation is not in standard form, you might need to complete the square to get it into standard form before you can identify the center and radius.

• Use a compass for more accurate circles, especially if graphing by hand. See the Geometry concept.