6x^2-3y^2-6x-3y+78=0

Lösung

6 x^{2} - 3 y^{2} - 6 x - 3 y + 78 = 0

(h, k) = (\frac{1}{2}, - \frac{1}{2}), a = \frac{103}{2}, b = \frac{103}{2 2}

Schritte zur Lösung

6 x^{2} - 3 y^{2} - 6 x - 3 y + 78 = 0

Rewrite

6 x^{2} - 3 y^{2} - 6 x - 3 y + 78 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{103}{2} ) ^{2}} - \frac{( x - \frac{1}{2} ) ^{2}}{( \frac{103}{2 2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, - \frac{1}{2}), a = \frac{103}{2}, b = \frac{103}{2 2}

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

16 x^{2} - 9 y^{2} - 96 x - 18 y - 9 = 0

x^{2} - y^{2} - 6 x + 4 y = - 4

x^{(2)} - y^{(2)} - 2 x + 4 y - 6 = 0

\frac{x ^{2}}{16} - \frac{y ^{2}}{49} = 1