y^2-3x^2-y+16x=9

解

y^{2} - 3 x^{2} - y + 16 x = 9

(h, k) = (\frac{8}{3}, \frac{1}{2}), a = \frac{145}{6}, b = \frac{145}{2 3}

解答ステップ

y^{2} - 3 x^{2} - y + 16 x = 9

y^{2} - 3 x^{2} - y + 16 x = 9

を標準的な双曲線のequationで書き換える

\frac{( x - \frac{8}{3} ) ^{2}}{( \frac{145}{6} ) ^{2}} - \frac{( y - \frac{1}{2} ) ^{2}}{( \frac{145}{2 3} ) ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (\frac{8}{3}, \frac{1}{2}), a = \frac{145}{6}, b = \frac{145}{2 3}