9x^2-9y^2-6x+24y=19

解

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

(h, k) = (\frac{1}{3}, \frac{4}{3}), a = \frac{2}{3}, b = \frac{2}{3}

解答ステップ

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

を標準的な双曲線のequationで書き換える

\frac{( x - \frac{1}{3} ) ^{2}}{( \frac{2}{3} ) ^{2}} - \frac{( y - \frac{4}{3} ) ^{2}}{( \frac{2}{3} ) ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (\frac{1}{3}, \frac{4}{3}), a = \frac{2}{3}, b = \frac{2}{3}