8y^2+3y-9=8x^2+9x-3

解

8 y^{2} + 3 y - 9 = 8 x^{2} + 9 x - 3

(h, k) = (- \frac{9}{16}, - \frac{3}{16}), a = \frac{15}{4 2}, b = \frac{15}{4 2}

解答ステップ

8 y^{2} + 3 y - 9 = 8 x^{2} + 9 x - 3

8 y^{2} + 3 y - 9 - 8 x^{2} - 9 x + 3 = 0

を標準的な双曲線のequationで書き換える

\frac{( y - ( - \frac{3}{16} ) ) ^{2}}{( \frac{15}{4 2} ) ^{2}} - \frac{( x - ( - \frac{9}{16} ) ) ^{2}}{( \frac{15}{4 2} ) ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (- \frac{9}{16}, - \frac{3}{16}), a = \frac{15}{4 2}, b = \frac{15}{4 2}