(8(x^2-1/4))/(9/2)-9y^2 9/2 =(9/2)/(9/2)

解

\frac{8 ( x ^{2} - \frac{1}{4} )}{\frac{9}{2}} - 9 y^{2} \frac{9}{2} = \frac{\frac{9}{2}}{\frac{9}{2}}

(h, k) = (0, 0), a = \frac{13}{4}, b = \frac{26}{27}

解答ステップ

\frac{8 ( x ^{2} - \frac{1}{4} )}{\frac{9}{2}} - 9 y^{2} \frac{9}{2} = \frac{\frac{9}{2}}{\frac{9}{2}}

\frac{8 ( x ^{2} - \frac{1}{4} )}{\frac{9}{2}} - 9 y^{2} \frac{9}{2} = \frac{\frac{9}{2}}{\frac{9}{2}}

を標準的な双曲線のequationで書き換える

\frac{( x - 0 ) ^{2}}{( \frac{13}{4} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{26}{27} ) ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (0, 0), a = \frac{13}{4}, b = \frac{26}{27}