center 0=9y^2-x^2+2x+72y+125

Lösung

center

0 = 9 y^{2} - x^{2} + 2 x + 72 y + 125

(1, - 4)

Schritte zur Lösung

0 = 9 y^{2} - x^{2} + 2 x + 72 y + 125

Rewrite

0 - 9 y^{2} + x^{2} - 2 x - 72 y - 125 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 4), a = 2, b = 32

And the center is:

(1, - 4)

ce n t er 9 x^{2} - 9 y^{2} - 18 x + 54 = 0

ce n t er \frac{( x - 3 ) ^{2}}{49} - \frac{( y - 5 ) ^{2}}{25} = 1

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

ce n t er \frac{( x - 3 ) ^{2}}{a ^{2}} - \frac{( y - 4 ) ^{2}}{b ^{2}} = 1

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