4x^2-16y^2-10x+21y-27=0

解

4 x^{2} - 16 y^{2} - 10 x + 21 y - 27 = 0

(h, k) = (\frac{5}{4}, \frac{21}{32}), a = \frac{1687}{16}, b = \frac{1687}{32}

解答ステップ

4 x^{2} - 16 y^{2} - 10 x + 21 y - 27 = 0

4 x^{2} - 16 y^{2} - 10 x + 21 y - 27 = 0

を標準的な双曲線のequationで書き換える

\frac{( x - \frac{5}{4} ) ^{2}}{( \frac{1687}{16} ) ^{2}} - \frac{( y - \frac{21}{32} ) ^{2}}{( \frac{1687}{32} ) ^{2}} = 1

ゆえに双曲線の特性は:

(h, k) = (\frac{5}{4}, \frac{21}{32}), a = \frac{1687}{16}, b = \frac{1687}{32}