asymptoten 3x^2-8y^2+12x+16y+20=0

Lösung

asymptoten

3 x^{2} - 8 y^{2} + 12 x + 16 y + 20 = 0

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

Schritte zur Lösung

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

Calculate Hyperbola properties

3 x^{2} - 8 y^{2} + 12 x + 16 y + 20 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, 1), a = 2, b = \frac{4}{3}

y = \frac{2}{\frac{4}{3}} (x - (- 2)) + 1, y = - \frac{2}{\frac{4}{3}} (x - (- 2)) + 1

Fasse zusammen

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

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

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

a sy m pt o t es - 9 x^{2} + 4 y^{2} = 36

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

a sy m pt o t es 16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0