100x^2+112952x-100y^2-106y=48838

Lösung

100 x^{2} + 112952 x - 100 y^{2} - 106 y = 48838

(h, k) = (- \frac{14119}{25}, - \frac{53}{100}), a = \frac{3194419567}{100}, b = \frac{3194419567}{100}

Schritte zur Lösung

100 x^{2} + 112952 x - 100 y^{2} - 106 y = 48838

Rewrite

100 x^{2} + 112952 x - 100 y^{2} - 106 y = 48838

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{14119}{25} ) ) ^{2}}{( \frac{3194419567}{100} ) ^{2}} - \frac{( y - ( - \frac{53}{100} ) ) ^{2}}{( \frac{3194419567}{100} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{14119}{25}, - \frac{53}{100}), a = \frac{3194419567}{100}, b = \frac{3194419567}{100}

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

9 x^{2} - 4 y^{2} + 18 x - 24 y + 9 = 0

x^{2} - y^{2} + 8 x - 2 y + 14 = 0

x^{2} - y^{2} = 5

y^{2} - x^{2} = 2