asymptoten (x/2)^2-(y/3)^2=1

Lösung

asymptoten

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

y = \frac{3 x}{2}, y = - \frac{3 x}{2}

Schritte zur Lösung

y = \pm \frac{b}{a} (x - h) + k

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (0, 0), a = 2, b = 3

y = \frac{3}{2} (x - 0) + 0, y = - \frac{3}{2} (x - 0) + 0

Fasse zusammen

y = \frac{3 x}{2}, y = - \frac{3 x}{2}

a sy m pt o t es \frac{x ^{2}}{4} - \frac{y ^{2}}{36} = 1

a sy m pt o t es \frac{x ^{2}}{25} - \frac{y ^{2}}{64} = 1

a sy m pt o t es \frac{y ^{2}}{4} - x^{2} = 1

a sy m pt o t es y^{2} - 4 x^{2} + 4 x - 2 y - 4 = 0

a sy m pt o t es 16 y^{2} - x^{2} + 2 x + 64 y - 1 = 0