((x^{(2)}))/((144))-((y^{(2)}))/((81))=1

解答

\frac{( x ^{(2)} )}{( 144 )} - \frac{( y ^{(2)} )}{( 81 )} = 1

(h, k) = (0, 0), a = 12, b = 9

求解步骤

\frac{x ^{2}}{144} - \frac{y ^{2}}{81} = 1

将

\frac{x ^{2}}{144} - \frac{y ^{2}}{81} = 1

改写为标准双曲线方程形式

\frac{( x - 0 ) ^{2}}{1 2 ^{2}} - \frac{( y - 0 ) ^{2}}{9 ^{2}} = 1

因此双曲线的性质为:

(h, k) = (0, 0), a = 12, b = 9

9 x^{(2)} - 4 y^{(2)} + 18 x - 27 = 0

4 x^{2} - 5 y^{2} - 16 x - 30 y - 9 = 0

\frac{( x - 1.6 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{2} = 1

\frac{( x - 4 ) ^{2}}{144} - \frac{( y - 11 ) ^{2}}{25} = 1

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