Question

Every point on a circle the same distance from the center of the circle. If (x, y) represents any point on a circle and (5,2) is the center of the circle, use the Distance Formula to represent the length of the radius r of the circle

Answer 1

First, we can draw a picture to understand more easily what the exercise asks of us.

We must find the radius of the circle and this is precisely the distance from the point (5,2) to the origin. Then using the Distance Formula, we have:

`\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(5-0)^2+(2-0)^2} \\ d=\sqrt[]{(5)^2+(2)^2} \\ d=\sqrt[]{25+4} \\ d=\sqrt[]{29} \end{gathered}`

Where

`\begin{gathered} (x_1,y_1)\Rightarrow(0,0) \\ (x_2,y_2)\Rightarrow(5,2) \end{gathered}`

However, if we take it the other way around, we arrive at the same answer. Finally, from what is shown in the previous graph

`\begin{gathered} r=d \\ r=\sqrt[]{29} \end{gathered}`