How can I determine the radius of a circle represented on a graph?

by

Finding the radius of a circle on a graph is a straightforward process, especially if you have the equation of the circle or you can identify key points on the graph.

Here’s a step-by-step guide:

Method 1: Using the Circle’s Equation

If you know the equation of the circle, which is generally written in the form:

(x - h)² + (y - k)² = r²

In this equation:

  • (h, k) represents the center of the circle.
  • r stands for the radius.

To find the radius, you just need to:

  1. Identify the value of r² from the equation.
  2. Take the square root of r² to find r:
r = √(r²)

Method 2: Using Points on the Graph

If you don’t have the equation but can see the circle plotted on the graph:

  1. Identify the center of the circle, which is the point from which all points on the circle are equidistant.
  2. Select any point that lies on the circumference of the circle. Make note of its coordinates, (x,y).
  3. Calculate the distance between the center (h,k) and the point (x,y). The formula for distance between two points is:
d = √((x - h)² + (y - k)²)

In this case, d will equal the radius r.

Example

For instance, if the center of the circle is located at (2, 3) and you identify a point on the circumference at (5, 7), you can calculate:

r = √((5 - 2)² + (7 - 3)²)
  = √(3² + 4²)
  = √(9 + 16)
  = √25 = 5

Thus, the radius of the circle is 5 units.

Conclusion

By using either the circle’s equation or points on the graph, you can easily find the radius of a circle. This skill can be very useful in geometry and various real-world applications involving circular shapes.

Leave a Comment