\(P_{1}\)(\(x_{1}\), \(y_{1}\)), \(P_{2}\)(\(x_{2}\), \(y_{2}\)),
求める円の中心を (a, b) と置くと
(\(x_{1}\) - a\()^{2}\) + (\(y_{1}\) - b\()^{2}\) = \(r^{2}\),
(\(x_{2}\) - a\()^{2}\) + (\(y_{2}\) - b\()^{2}\) = \(r^{2}\).
辺々引いて
(\(x_{1}\) - a\()^{2}\) - (\(x_{2}\) - a\()^{2}\) + (\(y_{1}\) - b\()^{2}\) - (\(y_{2}\) - b\()^{2}\) = 0
((\(x_{1}\) - a) - (\(x_{2}\) - a))((\(x_{1}\) - a) + (\(x_{2}\) - a))
　((\(y_{1}\) - b) - (\(y_{2}\) - b))((\(y_{1}\) - b) + (\(y_{2}\) - b)) = 0
(\(x_{1}\) - \(x_{2}\))(-2a + \(x_{1}\) + \(x_{2}\)) + (\(y_{1}\) - \(y_{2}\))(-2b + \(y_{1}\) + \(y_{2}\)) = 0.
ここからは一般的にやるなら場合分けしないといけないが,
要するに a = 又は b = の形にして
(\(x_{1}\) - a\()^{2}\) + (\(y_{1}\) - b\()^{2}\) = \(r^{2}\)
に代入して解く, という形。

二元連立二次方程式を解く。