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# Equation of a Circle with Diameter Endpoints Calculator

What is a circle?Equation of a circle with diameter endpointsMore calculators to assist you!FAQs

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:

FAQs

### 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.

## Standard equation

(x − A)² + (y − B)² = C

## Parametric equation

x = A + r cos(α), y = B + r sin(α)

## General equation

x² + y² + Dx + Ey + F = 0