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Sagot :
Given the endpoints of the diameter are (16,-2) and (16,-4).
Find the center of the circle by finding the midpoint of the line segment joining (16, -2) and (16,-4).
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ =(\frac{16+16}{2},\frac{-2-4}{2}) \\ =(16,-3) \end{gathered}[/tex]Now, find the radius of the circle using the distance formula.
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ =\sqrt[]{(16-16)^2+(-4-(-2))^2} \\ =\sqrt[]{(-2)^2} \\ =2 \end{gathered}[/tex]Thus, the diameter of the circle is 2. Hence the radius is 1 unit.
The standard equation of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) is the center and r is the radius.
Substitute the obtained values into the equation.
[tex](x-16)^2+(y+3)^2=1[/tex]
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