焦点-(x^2)/(a^2)+(y^2)/(b^2)=1

解答

焦点

- \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

(0, a^{2} + b^{2}), (0, - a^{2} + b^{2})

求解步骤

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

计算双曲线性质

- \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 :

上下开口双曲线，

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

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

计算

c :

c = b^{2} + a^{2}

(0, 0 + b^{2} + a^{2}), (0, 0 - b^{2} + a^{2})

整理后得

(0, a^{2} + b^{2}), (0, - a^{2} + b^{2})

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

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