13x^2-14x-26=13y^2+18y-7

Lösung

13 x^{2} - 14 x - 26 = 13 y^{2} + 18 y - 7

(h, k) = (\frac{7}{13}, - \frac{9}{13}), a = \frac{215}{13}, b = \frac{215}{13}

Schritte zur Lösung

13 x^{2} - 14 x - 26 = 13 y^{2} + 18 y - 7

Rewrite

13 x^{2} - 14 x - 26 - 13 y^{2} - 18 y + 7 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{7}{13} ) ^{2}}{( \frac{215}{13} ) ^{2}} - \frac{( y - ( - \frac{9}{13} ) ) ^{2}}{( \frac{215}{13} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{7}{13}, - \frac{9}{13}), a = \frac{215}{13}, b = \frac{215}{13}

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

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