焦点 4y^2-x^2+2x+16y+7=0

解答

焦点

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

(1, - 2 + 10), (1, - 2 - 10)

求解步骤

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

计算双曲线性质

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0 :

上下开口双曲线，

(h, k) = (1, - 2), a = 2, b = 22

(1, - 2 + c), (1, - 2 - c)

计算

c :

c = 2^{2} + (22)^{2} : 10

(1, - 2 + 10), (1, - 2 - 10)

f oc i \frac{( y + 6 ) ^{2}}{36} - \frac{( x + 4 ) ^{2}}{48} = 1

f oc i 9 x^{2} - 4 y^{2} - 54 x - 16 y + 29 = 0

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

f oc i \frac{y ^{2}}{16} - \frac{x ^{2}}{1} = 1

f oc i y^{2} - 2 = x^{2} - 2 x