9x^2-7y^2-72y+144=0

解

9 x^{2} - 7 y^{2} - 72 y + 144 = 0

(h, k) = (0, - \frac{36}{7}), a = \frac{48}{7}, b = \frac{16}{7}

解答ステップ

9 x^{2} - 7 y^{2} - 72 y + 144 = 0

9 x^{2} - 7 y^{2} - 72 y + 144 = 0

を標準的な双曲線のequationで書き換える

\frac{( y - ( - \frac{36}{7} ) ) ^{2}}{( \frac{48}{7} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{16}{7} ) ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (0, - \frac{36}{7}), a = \frac{48}{7}, b = \frac{16}{7}