Question

How to find the radius of a circle using the distance formula.

Answer 1

Case: Deriving the equation of a circle isolating the radius

We know that the general equation for a circle is given as:

Method:

The distance between two points is given as:

`\begin{gathered} d=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ (x_1,y_1)\text{ is the center of the circle written as (a,b)} \\ (x_2,y_2)\text{ is any part of the circle written as (x,y)} \\ d=\text{ }\sqrt[]{(x_{}-a_{})^2+(y_{}-b_{})^2} \\ d\text{ is the distance betwe}en\text{ the center of the circle (a,b) and any parts of the circumference (x, y)} \\ \text{This means d is the radius, r} \\ r=\text{ }\sqrt[]{(x_{}-a_{})^2+(y_{}-b_{})^2} \end{gathered}`