500a^2=4368.932+500b^2

解

500 a^{2} = 4368.932 + 500 b^{2}

(h, k) = (0, 0), a = 2.95598 \dots, b = 2.95598 \dots

解答ステップ

500 a^{2} = 4368.932 + 500 b^{2}

500 a^{2} = 4368.932 + 500 b^{2}

を標準的な双曲線のequationで書き換える

\frac{( a - 0 ) ^{2}}{2.95598 \dots ^{2}} - \frac{( b - 0 ) ^{2}}{2.95598 \dots ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (0, 0), a = 2.95598 \dots, b = 2.95598 \dots