焦点 ((y-1)^2)/(1/4)-((x-1)^2)/(1/16)=1

解答

焦点

\frac{( y - 1 ) ^{2}}{\frac{1}{4}} - \frac{( x - 1 ) ^{2}}{\frac{1}{16}} = 1

(1, \frac{4 + 5}{4}), (1, \frac{4 - 5}{4})

求解步骤

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

计算双曲线性质

\frac{( y - 1 ) ^{2}}{\frac{1}{4}} - \frac{( x - 1 ) ^{2}}{\frac{1}{16}} = 1 :

上下开口双曲线，

(h, k) = (1, 1), a = \frac{1}{2}, b = \frac{1}{4}

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

计算

c :

c = (\frac{1}{2})^{2} + (\frac{1}{4})^{2} : \frac{5}{4}

(1, 1 + \frac{5}{4}), (1, 1 - \frac{5}{4})

整理后得

(1, \frac{4 + 5}{4}), (1, \frac{4 - 5}{4})

f oc i \frac{( X - 8 ) ^{2}}{9} - \frac{( Y + 3 ) ^{2}}{16} = 1

f oc i 4 x^{2} - 5 y^{2} - 32 x + 10 y + 79 = 0

f oc i \frac{( x + 2 ) ^{2}}{64} - \frac{( y + 4 ) ^{2}}{81} = 1

f oc i 4 x^{2} - 9 y^{2} - 16 x + 18 y - 7 = 0

f oc i x^{2} - 3 y^{2} + 2 x + 6 y - 1 = 0