To complete the equation of the circle, we need to determine the radius of the circle, since the equation provided is in standard form [tex]\((x-h)² + (y-k)² = r²\)[/tex], where [tex]\((h, k)\)[/tex] is the center of the circle and [tex]\(r\)[/tex] is the radius.
Given the equation:
[tex]\[
(x-3)² + (y-2)² = r²
\][/tex]
The center of the circle [tex]\((h, k)\)[/tex] is at [tex]\((3, 2)\)[/tex]. To complete this equation, we need the value of the radius [tex]\(r\)[/tex].
Since we don't have the radius provided in the question, we can only denote the equation in terms of the radius squared, [tex]\(r²\)[/tex].
Therefore, the equation of the circle is already complete in its current form, except for the explicit value of [tex]\(r²\)[/tex], which we will leave as [tex]\(r²\)[/tex]:
[tex]\[
(x-3)² + (y-2)² = r²
\][/tex]
In summary, the completed equation of the circle is:
[tex]\[
(x-3)² + (y-2)² = r²
\][/tex]
