foki 3x^2-15y^2+2x-3y=4

Lösung

foki

3 x^{2} - 15 y^{2} + 2 x - 3 y = 4

(\frac{- 5 6 + 3 251}{15 6}, - \frac{1}{10}), (\frac{- 5 6 - 3 251}{15 6}, - \frac{1}{10})

Schritte zur Lösung

(h + c, k), (h - c, k)

Calculate Hyperbola properties

3 x^{2} - 15 y^{2} + 2 x - 3 y = 4 :

Right-left Hyperbola with

(h, k) = (- \frac{1}{3}, - \frac{1}{10}), a = \frac{251}{6 5}, b = \frac{251}{30}

(- \frac{1}{3} + c, - \frac{1}{10}), (- \frac{1}{3} - c, - \frac{1}{10})

Compute

c :

c = (\frac{251}{6 5})^{2} + (\frac{251}{30})^{2} : \frac{251}{5 6}

(- \frac{1}{3} + \frac{251}{5 6}, - \frac{1}{10}), (- \frac{1}{3} - \frac{251}{5 6}, - \frac{1}{10})

Fasse zusammen

(\frac{- 5 6 + 3 251}{15 6}, - \frac{1}{10}), (\frac{- 5 6 - 3 251}{15 6}, - \frac{1}{10})

f oc i \frac{y ^{2}}{4} - \frac{x ^{2}}{9} = 1

f oc i \frac{( x - 5 ) ^{2}}{1} - \frac{( y - 4 ) ^{2}}{1} = 1

f oc i 9 x^{2} - 4 y^{2} - 54 x - 8 y + 113 = 0

f oc i \frac{( y - 2 ) ^{2}}{9} - \frac{( x - 1 ) ^{2}}{16} = 1

f oc i x^{2} - 3 y^{2} + 12 = 0