19x^2-9y^2-64x-18y+199=0

Lösung

19 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

(h, k) = (\frac{32}{19}, - 1), a = \frac{4 61}{57}, b = \frac{4 183}{19}

Schritte zur Lösung

19 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

Rewrite

19 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 1 ) ) ^{2}}{( \frac{4 61}{57} ) ^{2}} - \frac{( x - \frac{32}{19} ) ^{2}}{( \frac{4 183}{19} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{32}{19}, - 1), a = \frac{4 61}{57}, b = \frac{4 183}{19}

a^{2} - b^{2} = 396

\frac{x ^{2}}{140} - \frac{( y - 6 ) ^{2}}{4} = - 1

\frac{( x - 27 ) ^{2}}{9} - \frac{( y - 4 ) ^{2}}{25} = 1

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

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