y^2-1=16(x^2-1)

解答

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

(h, k) = (0, 0), a = \frac{15}{4}, b = 15

求解步骤

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

将

y^{2} - 1 - 16 (x^{2} - 1) = 0

改写为标准双曲线方程形式

\frac{( x - 0 ) ^{2}}{( \frac{15}{4} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 15 ) ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = \frac{15}{4}, b = 15

5 x^{2} - 4 y^{2} - 18 y + 9 = 0

\frac{( x + 3 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{9} = 1

\frac{( y + 3 ) ^{2}}{81} - \frac{( x + 3 ) ^{2}}{16} = 1

(x - 4)^{2} - (y - 4)^{2} \leq 9

x^{2} + x = y^{2}