Answer:
[tex](x-2)^2 +(y-4)^2=25[/tex]
Step-by-step explanation:
Since, the diameter of the circle having the end points (-2, 1) and (6, 7),
Thus, by the distance formula,
[tex]\text{Diameter}=\sqrt{(6+2)^2+(7-1)^2}[/tex]
[tex]=\sqrt{8^2+6^2}[/tex]
[tex]=\sqrt{64+36}[/tex]
[tex]=\sqrt{100}[/tex]
[tex]=10\text{ unit}[/tex]
So, the radius of the circle = [tex]\frac{10}{2}[/tex] = 5 unit,
Let the equation of the circle is,
[tex](x-h)^2+(y-k)^2=25[/tex]
Where, (h, k) is the center of the circle,
Since, points (-2, 1) and (6, 7) are on the circle,
They must satisfy the equation of the circle,
[tex](-2-h)^2+(1-k)^2 = 25[/tex]
[tex](6-h)^2+(7-k)^2=25[/tex]
By solving these equations,
We get,
h = 2, k = 4
Hence, the equation of the circle would be,
[tex](x-2)^2 +(y-4)^2=25[/tex]
