数学 – 図形と数式の関係 - 平面図形と式 – 円と軌跡(円の方程式, 中心, 半径)

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数学読本〈2〉簡単な関数/平面図形と式/指数関数・対数関数/三角関数 (松坂和夫(著)、岩波書店)の第6章(図形と数式の関係 - 平面図形と式)、6.3(円と軌跡)、円の方程式、問19.を解いてみる。

問19.

$x^{2} + y^{2} = 9$
${(x - 1)}^{2} + {(x + 3)}^{2} = 16$
$\begin{array}{l} {(x + 3)}^{2} + {(x - 2)}^{2} = 9 + 4 \\ {(x + 3)}^{2} + {(x - 2)}^{2} = 13 \end{array}$
$\begin{array}{l} 4 r^{2} = 4^{2} + 2^{2} = 20 \\ r^{2} = 5 \\ (3, 3) \\ {(x - 3)}^{2} + {(x - 3)}^{2} = 5 \end{array}$
$\begin{array}{l} (a, b) \\ a + b = 3 \\ b = 3 - a \\ {(a - 4)}^{2} + {(b - 1)}^{2} = {(a - 2)}^{2} + {(b + 3)}^{2} \\ - 8 a + 16 - 2 b + 1 = - 4 a + 4 + 6 b + 9 \\ - 4 a - 8 b = - 4 \\ - 4 a - 24 + 8 a = - 4 \\ a = 5 \\ b = - 2 \\ r^{2} = 1 + 9 = 10 \\ {(x - 5)}^{2} + {(x + 2)}^{2} = 10 \end{array}$

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