Given:
It is given that a circle is represented by two end points (5,1) and (3,-1).
Find:
we have to find the equation of the circle, radius and center of the circle using end points.
Explanation:
The circle represented by two end points (5,1) and (3,-1) is drawn as
The diameter of the circle is
[tex]d=\sqrt{(5-3)^2+(1-(-1))^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}[/tex]
Therefore radius of the circle is
[tex]B3=\frac{d}{2}=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex]
The center of the circle is
[tex](B1,B2)=(\frac{5+3}{2},\frac{1-1}{2})=(\frac{8}{2},\frac{0}{2})=(4,0)[/tex]
Therefore, the equation of the circle is
[tex](x-4)^2+(y-0)^2=(\sqrt{2})^2[/tex]
where,
[tex]\begin{gathered} B1=4 \\ B2=0 \\ B3=\sqrt{2} \end{gathered}[/tex]
