18x^2-32y^2-108y-128x-254=0^2

Lösung

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0^{2}

(h, k) = (\frac{32}{9}, - \frac{27}{16}), a = \frac{28111}{36}, b = \frac{28111}{48}

Schritte zur Lösung

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0^{2}

Rewrite

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0^{2}

in the form of a standard hyperbola equation

\frac{( x - \frac{32}{9} ) ^{2}}{( \frac{28111}{36} ) ^{2}} - \frac{( y - ( - \frac{27}{16} ) ) ^{2}}{( \frac{28111}{48} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{32}{9}, - \frac{27}{16}), a = \frac{28111}{36}, b = \frac{28111}{48}

\frac{x ^{2}}{5} - \frac{y ^{2}}{1} = 1

3 y^{2} - x^{2} + 18 y + 4 x + 28 = 0

\frac{50}{x + y} + \frac{8}{x - y} = 7

4 x^{2} - 9 y^{2} - 16 x + 36 y = 56

so l v e f or x, \frac{x ^{2}}{4} + 1 = 3 m (x)^{2} - 1