焦点 100x^2+112952x-100y^2-106y=48838

解答

焦点

100 x^{2} + 112952 x - 100 y^{2} - 106 y = 48838

(\frac{- 28238 2 + 3194419567}{50 2}, - \frac{53}{100}), (\frac{- 28238 2 - 3194419567}{50 2}, - \frac{53}{100})

求解步骤

(h + c, k), (h - c, k)

计算双曲线性质

100 x^{2} + 112952 x - 100 y^{2} - 106 y = 48838 :

左右开口双曲线，

(h, k) = (- \frac{14119}{25}, - \frac{53}{100}), a = \frac{3194419567}{100}, b = \frac{3194419567}{100}

(- \frac{14119}{25} + c, - \frac{53}{100}), (- \frac{14119}{25} - c, - \frac{53}{100})

计算

c :

c = (\frac{3194419567}{100})^{2} + (\frac{3194419567}{100})^{2} : \frac{3194419567}{50 2}

(- \frac{14119}{25} + \frac{3194419567}{50 2}, - \frac{53}{100}), (- \frac{14119}{25} - \frac{3194419567}{50 2}, - \frac{53}{100})

整理后得

(\frac{- 28238 2 + 3194419567}{50 2}, - \frac{53}{100}), (\frac{- 28238 2 - 3194419567}{50 2}, - \frac{53}{100})

f oc i 4 x^{2} - 25 y^{2} + 16 x + 50 y - 109 = 0

f oc i 9 x^{2} - 18 x - 24 y - 63 = 4 y^{2}

f oc i 36 x^{2} - 25 y^{2} = 900

f oc i \frac{x ^{2}}{36} - \frac{y ^{2}}{4} = 1

f oc i - 9 x^{2} - 32 y = - 16 y^{2} + 128