焦点 10y^2-5x^2=50

解答

焦点

10 y^{2} - 5 x^{2} = 50

(0, 15), (0, - 15)

求解步骤

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

计算双曲线性质

10 y^{2} - 5 x^{2} = 50 :

上下开口双曲线，

(h, k) = (0, 0), a = 5, b = 10

(0, 0 + c), (0, 0 - c)

计算

c :

c = 5^{2} + 10^{2} : 15

(0, 0 + 15), (0, 0 - 15)

整理后得

(0, 15), (0, - 15)

f oc i \frac{( x - 1 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

f oc i 2 x^{2} - 7 y^{2} - 16 x + 14 y = - 11

f oc i 9 x^{2} - 4 y^{2} - 36 x + 8 y - 4 = 0

f oc i \frac{( x - h ) ^{2}}{64} - \frac{( y - k ) ^{2}}{9} = 1

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