The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the points A(-1, 7) and B(7, 7). AB is a diameter of a circle.
The midpoint of diameter is a center of a circle.
Calculate this using:
[tex]M\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}[/tex]
Substitute
[tex]M\left(\dfrac{-1+7}{2},\ \dfrac{7+7}{2}\right)\to M(3,\ 7)[/tex]
Therefore we have h = 3 and k = 7.
Calculate a length of a radius using:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute coordinates of the points (3, 7) and (7, 7):
[tex]r=\sqrt{(7-3)^2+(7-7)^2}=\sqrt{4^2}=4[/tex]
Your answer is:
[tex](x-3)^2+(y-7)^2=4^2\\\\\boxed{(x-3)^2+(y-7)^2=16}[/tex]
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You can read the coordinates of the center and length of a radius from a graph.
Look at the picture.
