25x^2+56476x-25y^2-3y=48838

Lösung

25 x^{2} + 56476 x - 25 y^{2} - 3 y = 48838

(h, k) = (- \frac{28238}{25}, - \frac{3}{50}), a = \frac{3194422367}{50}, b = \frac{3194422367}{50}

Schritte zur Lösung

25 x^{2} + 56476 x - 25 y^{2} - 3 y = 48838

Rewrite

25 x^{2} + 56476 x - 25 y^{2} - 3 y = 48838

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{28238}{25} ) ) ^{2}}{( \frac{3194422367}{50} ) ^{2}} - \frac{( y - ( - \frac{3}{50} ) ) ^{2}}{( \frac{3194422367}{50} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{28238}{25}, - \frac{3}{50}), a = \frac{3194422367}{50}, b = \frac{3194422367}{50}

x^{2} - y^{2} < 72

(\frac{y ^{2}}{16}) - (\frac{x ^{2}}{4}) = 1

3 x^{2} - y^{2} - 2 x - 4 = 0

27 x^{2} - 36 y^{2} - 216 x - 72 y + 225 = 0

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