10x^2-7y^2-30x+14y=5

解

10 x^{2} - 7 y^{2} - 30 x + 14 y = 5

(h, k) = (\frac{3}{2}, 1), a = \frac{41}{2 5}, b = \frac{41}{14}

解答ステップ

10 x^{2} - 7 y^{2} - 30 x + 14 y = 5

10 x^{2} - 7 y^{2} - 30 x + 14 y = 5

を標準的な双曲線のequationで書き換える

\frac{( x - \frac{3}{2} ) ^{2}}{( \frac{41}{2 5} ) ^{2}} - \frac{( y - 1 ) ^{2}}{( \frac{41}{14} ) ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (\frac{3}{2}, 1), a = \frac{41}{2 5}, b = \frac{41}{14}