8x^2-4y^2+10x-6y-8=0

Lösung

8 x^{2} - 4 y^{2} + 10 x - 6 y - 8 = 0

(h, k) = (- \frac{5}{8}, - \frac{3}{4}), a = \frac{71}{8}, b = \frac{71}{4 2}

Schritte zur Lösung

8 x^{2} - 4 y^{2} + 10 x - 6 y - 8 = 0

Rewrite

8 x^{2} - 4 y^{2} + 10 x - 6 y - 8 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{5}{8} ) ) ^{2}}{( \frac{71}{8} ) ^{2}} - \frac{( y - ( - \frac{3}{4} ) ) ^{2}}{( \frac{71}{4 2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{5}{8}, - \frac{3}{4}), a = \frac{71}{8}, b = \frac{71}{4 2}

\frac{x ^{2}}{4} - \frac{y ^{2}}{5} = 1

\frac{( x - 5 ) ^{2}}{16} - \frac{( y + 7 ) ^{2}}{9} = - 1

2 x^{2} - y^{2} - 1 = 0

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 2 ) ^{2}}{5} = 1

\frac{( x - 3 ) ^{2}}{49} - \frac{( y + 5 ) ^{2}}{25} = 1