Answer:
[tex](x-2)^{2}+(y-4)^{2}=25[/tex]
Step-by-step explanation:
step 1
Find the diameter of the circle
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-2,1)\\B(6,7)[/tex]
substitute the values
[tex]d=\sqrt{(7-1)^{2}+(6+2)^{2}}[/tex]
[tex]d=\sqrt{(6)^{2}+(8)^{2}}[/tex]
[tex]d=\sqrt{100}[/tex]
[tex]d=10\ units[/tex]
The radius is half the diameter
so
[tex]r=10/2=5\ units[/tex]
step 2
Find the center of the circle
the center of the circle is the midpoint between the endpoints of the diameter
so
The center is
[tex](\frac{-2+6}{2},\frac{1+7}{2})[/tex]
[tex](2,4)[/tex]
step 3
Find the equation of the circle
The equation of the circle is
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
substitute the values
[tex](x-2)^{2}+(y-4)^{2}=5^{2}[/tex]
[tex](x-2)^{2}+(y-4)^{2}=25[/tex]
