center 4x^2-1/2 y^2+8x+2y-2=0

Lösung

center

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

(- 1, 2)

Schritte zur Lösung

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

Rewrite

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 2), a = 1, b = 22

And the center is:

(- 1, 2)

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

ecce n t r i c i t y 9 x^{2} - 18 x - 24 y - 63 = 4 y^{2}

ecce n t r i c i t y \frac{( x - 1 ) ^{2}}{4} - \frac{( y - 2 ) ^{2}}{1} = 1

ecce n t r i c i t y 9 x^{2} - 36 x - 4 y^{2} - 24 y - 36 = 0

ecce n t r i c i t y \frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1