1/2 y^2-2y= 3/2 x^2-5x

Lösung

\frac{1}{2} y^{2} - 2 y = \frac{3}{2} x^{2} - 5 x

(h, k) = (\frac{5}{3}, 2), a = \frac{13}{3}, b = \frac{13}{3}

Schritte zur Lösung

\frac{1}{2} y^{2} - 2 y = \frac{3}{2} x^{2} - 5 x

Rewrite

\frac{1}{2} y^{2} - 2 y = \frac{3}{2} x^{2} - 5 x

in the form of a standard hyperbola equation

\frac{( x - \frac{5}{3} ) ^{2}}{( \frac{13}{3} ) ^{2}} - \frac{( y - 2 ) ^{2}}{( \frac{13}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{5}{3}, 2), a = \frac{13}{3}, b = \frac{13}{3}

\frac{x ^{2}}{49} - \frac{y ^{2}}{44} = 1

x^{2} - y^{2} = 640

- \frac{1}{2} (\frac{x ^{2}}{2} - 100 x) + C = - 3 y^{2} + 150 y + C

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

9 x^{2} - 4 y^{2} - 36 x - 16 x + 20 = 0