焦点 4y^2-9x^2+40y-540x-8036=0

解答

焦点

4 y^{2} - 9 x^{2} + 40 y - 540 x - 8036 = 0

(- 30, - 5 + 13), (- 30, - 5 - 13)

求解步骤

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

计算双曲线性质

4 y^{2} - 9 x^{2} + 40 y - 540 x - 8036 = 0 :

上下开口双曲线，

(h, k) = (- 30, - 5), a = 3, b = 2

(- 30, - 5 + c), (- 30, - 5 - c)

计算

c :

c = 3^{2} + 2^{2} : 13

(- 30, - 5 + 13), (- 30, - 5 - 13)

f oc i \frac{x ^{2}}{49} - y^{2} = 1

f oc i 4 x^{2} - 4 y^{2} + 20 x - 16 y + 25 = 0

f oc i \frac{x ^{2}}{25} - \frac{y ^{2}}{81} = 1

f oc i 3 x^{2} - 4 y^{2} = 12

f oc i 5 x^{2} - 5 y^{2} + 20 x - 60 y = 185