4a2-9b2=(2a2+3b2)(2a2-3b2)

解

4 a 2 - 9 b 2 = (2 a 2 + 3 b 2) (2 a 2 - 3 b 2)

(h, k) = (\frac{1}{4}, \frac{1}{4}), a = \frac{5}{12}, b = \frac{5}{8}

解答ステップ

4 a \cdot 2 - 9 b \cdot 2 = (2 a \cdot 2 + 3 b \cdot 2) (2 a \cdot 2 - 3 b \cdot 2)

4 a 2 - 9 b 2 - (2 a 2 + 3 b 2) (2 a 2 - 3 b 2) = 0

を標準的な双曲線のequationで書き換える

\frac{( b - \frac{1}{4} ) ^{2}}{( \frac{5}{12} ) ^{2}} - \frac{( a - \frac{1}{4} ) ^{2}}{( \frac{5}{8} ) ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (\frac{1}{4}, \frac{1}{4}), a = \frac{5}{12}, b = \frac{5}{8}