离心率-((x-2)^2)/5+((y+1)^2)/9 =1

解答

离心率

- \frac{( x - 2 ) ^{2}}{5} + \frac{( y + 1 ) ^{2}}{9} = 1

\frac{14}{3}

十进制

1.24721 \dots

求解步骤

= \frac{a ^{2} + b ^{2}}{a}

计算双曲线性质

- \frac{( x - 2 ) ^{2}}{5} + \frac{( y + 1 ) ^{2}}{9} = 1 :

上下开口双曲线，

(h, k) = (2, - 1), a = 3, b = 5

= \frac{3 ^{2} + ( 5 ) ^{2}}{3}

整理后得

= \frac{14}{3}

ecce n t r i c i t y \frac{x ^{2}}{58} - \frac{y ^{2}}{174} = 1

ecce n t r i c i t y \frac{x ^{2}}{4} - \frac{y ^{2}}{9} = 1

ecce n t r i c i t y 25 x^{2} + 10922 x - 25 y^{2} - y^{2} = 1439

ecce n t r i c i t y 16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

ecce n t r i c i t y 16 y^{2} - 32 y - 9 x^{2} - 18 x = 137