Graphing a Circle: Step-by-Step Guide with Formula and Examples

Graph Circle Formula

To graph a circle using its equation, you need to determine the center coordinates and the radius

To graph a circle using its equation, you need to determine the center coordinates and the radius. The formula for a circle in standard form is:

(x – h)^2 + (y – k)^2 = r^2

Where (h, k) represents the center coordinates of the circle, and r represents the radius.

Here’s a step-by-step process to graph a circle:

Step 1: Identify the center coordinates (h, k) of the circle.
In the equation (x – h)^2 + (y – k)^2 = r^2, the values of h and k represent the x and y coordinates of the center of the circle.

Step 2: Determine the radius, r.
The radius is the distance from the center of the circle to any point on the circumference. In the equation, r^2 represents the square of the radius. To find the radius, take the square root of r^2 (if it’s given as a squared number).

Step 3: Plot the center on a coordinate plane.
Using the coordinates (h, k), plot the center of the circle. This will be a point on the coordinate plane.

Step 4: Determine additional points on the circumference.
To plot more points on the circumference, choose any x-coordinate and substitute it into the equation to solve for y. You can also choose any y-coordinate and substitute it into the equation to solve for x.

Step 5: Connect the points to form the circle.
Once you have a few points on the circumference, connect them using a smooth, curved line to complete the circle.

Let’s consider an example:
Suppose you have the equation (x – 3)^2 + (y + 2)^2 = 9.

Step 1: Identify the center coordinates.
The center coordinates are (3, -2).

Step 2: Determine the radius.
In this case, the radius is 3 because r^2 is equal to 9, so the radius is the square root of 9, which is 3.

Step 3: Plot the center.
On a coordinate plane, locate the point (3, -2) and plot it.

Step 4: Determine additional points.
Choose various x or y-coordinates and substitute them into the equation to solve for the corresponding y or x. For example:
If x = 4, then (4 – 3)^2 + (y + 2)^2 = 9
Simplifying, we get (1)^2 + (y + 2)^2 = 9
This leads to (y + 2)^2 = 8
Taking the square root, we have y + 2 = ±√8
Simplifying further, y = -2 ± √8

Similarly, you can find more points on the circumference by substituting other x or y-values.

Step 5: Connect the points.
Using the determined points, connect them with a curved line to form the circle.

Remember to label the center and the radius on your graph.

That’s how you graph a circle using its equation.

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