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

解

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

(h, k) = (- \frac{1}{3}, \frac{3}{4}), a = \frac{67}{4 3}, b = \frac{67}{6 2}

解答ステップ

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

3 x^{2} + 2 y + x - 2 y^{2} + y + x + 2 = 0

を標準的な双曲線のequationで書き換える

\frac{( y - \frac{3}{4} ) ^{2}}{( \frac{67}{4 3} ) ^{2}} - \frac{( x - ( - \frac{1}{3} ) ) ^{2}}{( \frac{67}{6 2} ) ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (- \frac{1}{3}, \frac{3}{4}), a = \frac{67}{4 3}, b = \frac{67}{6 2}