((y-4)^2)/(16)-((x+3)^2)/(36)=1

解答

\frac{( y - 4 ) ^{2}}{16} - \frac{( x + 3 ) ^{2}}{36} = 1

(h, k) = (- 3, 4), a = 4, b = 6

求解步骤

\frac{( y - 4 ) ^{2}}{16} - \frac{( x + 3 ) ^{2}}{36} = 1

将

\frac{( y - 4 ) ^{2}}{16} - \frac{( x + 3 ) ^{2}}{36} = 1

改写为标准双曲线方程形式

\frac{( y - 4 ) ^{2}}{4 ^{2}} - \frac{( x - ( - 3 ) ) ^{2}}{6 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (- 3, 4), a = 4, b = 6

\frac{y}{4 x ^{2} - 9 y ^{2}} = 36

\frac{( x - 7 ) ^{2}}{16} - \frac{y ^{2}}{9} = 1

16 x^{2} - 32 x = 9 y^{2} + 144 y - 16

y^{(2)} - x^{(2)} = (\frac{1}{49})

9 x^{2} - 4 y^{2} - 72 x + 8 y + 17 = 0