asymptoten x^2-y^2-4x+8y-21=0

Lösung

asymptoten

x^{2} - y^{2} - 4 x + 8 y - 21 = 0

y = x + 2, y = - (x - 2) + 4

Schritte zur Lösung

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

Calculate Hyperbola properties

x^{2} - y^{2} - 4 x + 8 y - 21 = 0 :

Right-left Hyperbola with

(h, k) = (2, 4), a = 3, b = 3

y = \frac{3}{3} (x - 2) + 4, y = - \frac{3}{3} (x - 2) + 4

Fasse zusammen

y = x + 2, y = - (x - 2) + 4

a sy m pt o t es \frac{x ^{2}}{7} - \frac{7 y ^{2}}{42} = 1

a sy m pt o t es \frac{x ^{2}}{81} - \frac{y ^{2}}{9} = 1

a sy m pt o t es \frac{y ^{2}}{4} - \frac{x ^{2}}{9} = 1

a sy m pt o t es \frac{y ^{2}}{25} - \frac{x ^{2}}{16} = 1

a sy m pt o t es 3 x^{2} - 15 y^{2} + 2 x - 3 y = 4