center-6x^2+4y^2+6x+16y-1=0

Lösung

center

- 6 x^{2} + 4 y^{2} + 6 x + 16 y - 1 = 0

(\frac{1}{2}, - 2)

Schritte zur Lösung

- 6 x^{2} + 4 y^{2} + 6 x + 16 y - 1 = 0

Rewrite

- 6 x^{2} + 4 y^{2} + 6 x + 16 y - 1 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 2 ) ) ^{2}}{( \frac{31}{2 2} ) ^{2}} - \frac{( x - \frac{1}{2} ) ^{2}}{( \frac{31}{2 3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, - 2), a = \frac{31}{2 2}, b = \frac{31}{2 3}

And the center is:

(\frac{1}{2}, - 2)

ce n t er y^{2} - 4 x^{2} < 1

ce n t er - 9 x^{2} + 8 y^{2} + 36 x + 48 y = 36

ce n t er \frac{y ^{2}}{36} - \frac{x ^{2}}{16} = 1

ce n t er \frac{( x - 1 ) ^{2}}{9} - \frac{( y - 2 ) ^{2}}{16} = 1

ce n t er \frac{( y - 1 ) ^{2}}{9} - \frac{( x - 4 ) ^{2}}{25} = 1