3/2 (v-3/2)^2-1/2 (u+(sqrt(3))/2)^2=6

Lösung

\frac{3}{2} (v - \frac{3}{2})^{2} - \frac{1}{2} (u + \frac{3}{2})^{2} = 6

(h, k) = (\frac{3}{2}, - \frac{3}{2}), a = 2, b = 23

Schritte zur Lösung

\frac{3}{2} (v - \frac{3}{2})^{2} - \frac{1}{2} (u + \frac{3}{2})^{2} = 6

Rewrite

\frac{3}{2} (v - \frac{3}{2})^{2} - \frac{1}{2} (u + \frac{3}{2})^{2} = 6

in the form of a standard hyperbola equation

\frac{( v - \frac{3}{2} ) ^{2}}{2 ^{2}} - \frac{( u - ( - \frac{3}{2} ) ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{3}{2}, - \frac{3}{2}), a = 2, b = 23

2 x^{2} - 5 y^{2} = 13

\frac{( x - 2 ) ^{2}}{9} - \frac{( y + 3 ) ^{2}}{27} = 1

9 x^{2} - 4 y^{2} - 36 x = 0

(\frac{y - 4}{16})^{2} - (\frac{x + 3}{36})^{2} = 1

\frac{( y - 3 ) ^{2}}{25} - \frac{( x + 4 ) ^{2}}{36} = 1