# Equation of a Circle with Diameter Endpoints Calculator

Created by Vishnuvardhan Shakthibala
Reviewed by Krishna Nelaturu
Last updated: Apr 06, 2022

Do you have endpoints of a diameter? And are you looking for an easy way to find the equation of a circle? If you are saying YES, then our equation of a circle with diameter endpoints calculator is a perfect fit for you. Go on and insert the diameter endpoints in the indicated fields. You will obtain circle equations in standard, general, and parametric form.

• How to find the equation of a circle with diameter endpoints?; and
• How to use our equation of a circle with diameter endpoints calculator?

## What is a circle?

A circle is a 2-D closed geometrical shape whose boundary points are at an equal distance from the center of the geometry.

## Equation of a circle with diameter endpoints

To find the equation of a circle with diameter endpoints, you can use the following steps:

1. Find the distance between the endpoints $(x_1,y_1)$ and $(x_2,y_2)$ by using distance formula:
$\qquad \scriptsize d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}$
1. Divide $d$ by 2 to get the radius $r$ of the circle.
2. Next, you can use the midpoint formula to find the x coordinates $h$ and y coordinates $k$ for the circle's center. The equation is given as:
\qquad\qquad \scriptsize \begin{align*} h=\frac{(x_2+x_1)}{2} \\ k=\frac{(y_2+y_1)}{2} \end{align*}

By knowing the center coordinates: $h$,$k$, and radius $r$ we can get the circle equation in standard form. It is given as:

$\qquad \scriptsize (x-h)^2 +(y-k)^2=r^2$

## More calculators to assist you!

We have a fleet of calculators to help you solve any problems related to circles. You can choose the calculators below as per your needs:

## FAQ

### What is the equation of the circle whose diameter endpoints are (6,4) and (2,8)?

The equation of a circle is (x-4)² + (y-6)² = 8. You can find this equation by using the following steps:

1. Find the x-coordinate (h) & y-coordinate (k) of the center of the circle by taking the summation of x-coordinates & y-coordinates of the endpoints of the diameter respectively and dividing by 2.
2. Calculate the distance between (6,4) and (2,8) using the distance formula and divide by 2 to get the circle's radius.
3. Substitute the center coordinates and radius into a standard form to get the equation of the circle.

### What is the midpoint between the points (3,-6) and (4,7)?

The midpoint is (1.5,0.5). To calculate the midpoint coordinates: sum the corresponding coordinates, and divide by 2.

Vishnuvardhan Shakthibala
Endpoints of a diameter
x1
y1
x2
y2
(x - A)² + (y - B)² = C
A
B
C
x = A + r cos(α), y = B + r sin(α)
A
B
r
x² + y² + Dx + Ey + F = 0
D
E
F
Center coordinates
x-coordinate
y-coordinate
Circle properties
Diameter
Area
Circumference
People also viewed…

### Average rate of change

Average rate of change calculator helps find how one variable changes with respect to another.

### Car heat

The hot car calculator shows you how fast the interior of a car heats up during a summers day.

### Korean age

If you're wondering what would your age be from a Korean perspective, use this Korean age calculator to find out.

### Trapezoid perimeter

Find the perimeter of a trapezoid with any of the possible combination of inputs with our trapezoid perimeter calculator! 