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

Lösung

foki

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

(\frac{512 + 5 28111}{144}, - \frac{27}{16}), (\frac{512 - 5 28111}{144}, - \frac{27}{16})

Schritte zur Lösung

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

(\frac{32}{9} + c, - \frac{27}{16}), (\frac{32}{9} - c, - \frac{27}{16})

Compute

c :

c = (\frac{28111}{36})^{2} + (\frac{28111}{48})^{2} : \frac{5 28111}{144}

(\frac{32}{9} + \frac{5 28111}{144}, - \frac{27}{16}), (\frac{32}{9} - \frac{5 28111}{144}, - \frac{27}{16})

Fasse zusammen

(\frac{512 + 5 28111}{144}, - \frac{27}{16}), (\frac{512 - 5 28111}{144}, - \frac{27}{16})

f oc i \frac{y ^{2}}{15} - \frac{x ^{2}}{1} = 1

f oc i x^{2} - y^{2} + 7 x + 8 y = 5

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

f oc i 9 (y - 2)^{2} - 4 x^{2} = 36

f oc i \frac{x ^{2}}{4} - \frac{y ^{2}}{5} = 1