Circle Endpoint Calculator

Formula

To calculate the radius (\(r\)):

\[ r = \sqrt{(x - h)^2 + (y - k)^2} \]

Where:

\(r\) is the radius of the circle
\(x\) is the x-coordinate of the point on the circle
\(y\) is the y-coordinate of the point on the circle
\(h\) is the x-coordinate of the center of the circle
\(k\) is the y-coordinate of the center of the circle

What is a Circle Endpoint?

A circle endpoint refers to a point on the circumference of a circle. The circle is defined by its center (\(h, k\)) and its radius (\(r\)). The endpoint is any point (\(x, y\)) that lies on the circle’s boundary. The relationship between these points is given by the circle equation, which ensures that the distance from the center to any point on the circle is equal to the radius.

Example Calculation 1

Let's assume the following values:

X-coordinate of the Point (\(x\)) = 5
Y-coordinate of the Point (\(y\)) = 8
X-coordinate of the Center (\(h\)) = 2
Y-coordinate of the Center (\(k\)) = 3

Using the formula:

\[ r = \sqrt{(5 - 2)^2 + (8 - 3)^2} = \sqrt{3^2 + 5^2} = \sqrt{9 + 25} = \sqrt{34} \approx 5.83 \]

The radius is approximately 5.83.

Example Calculation 2

Let's assume the following values:

X-coordinate of the Point (\(x\)) = 7
Y-coordinate of the Point (\(y\)) = 4
X-coordinate of the Center (\(h\)) = 3
Y-coordinate of the Center (\(k\)) = 2

Using the formula:

\[ r = \sqrt{(7 - 3)^2 + (4 - 2)^2} = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20} \approx 4.47 \]

The radius is approximately 4.47.