center 4x^2-9y^2-16x+18y-11=0

Lösung

center

4 x^{2} - 9 y^{2} - 16 x + 18 y - 11 = 0

(2, 1)

Schritte zur Lösung

4 x^{2} - 9 y^{2} - 16 x + 18 y - 11 = 0

Rewrite

4 x^{2} - 9 y^{2} - 16 x + 18 y - 11 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

And the center is:

(2, 1)

ce n t er \frac{( y - 3 ) ^{2}}{11} - \frac{( x + 1 ) ^{2}}{5} = 1

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

ce n t er x^{2} - 5 y^{2} - 6 x - 10 y - 1 = 0

ce n t er 4 y^{2} = 4 x^{2} + 12 y - 69 + 32 x

ce n t er 4 x^{2} - 12 y^{2} - 24 x + 24 y + 51 = 0