x^2+2y+x=2y^2+3y+2x+2

Lösung

x^{2} + 2 y + x = 2 y^{2} + 3 y + 2 x + 2

(h, k) = (\frac{1}{2}, - \frac{1}{4}), a = \frac{17}{2 2}, b = \frac{17}{4}

Schritte zur Lösung

x^{2} + 2 y + x = 2 y^{2} + 3 y + 2 x + 2

Rewrite

x^{2} + 2 y + x - 2 y^{2} - 3 y - 2 x - 2 = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{17}{2 2} ) ^{2}} - \frac{( y - ( - \frac{1}{4} ) ) ^{2}}{( \frac{17}{4} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, - \frac{1}{4}), a = \frac{17}{2 2}, b = \frac{17}{4}

- 4 x^{2} + 24 x + 16 y^{2} - 128 y + 156 = 0

(x + y) (x - y) - 2 = 0

\frac{y ^{2}}{a ^{2}} - \frac{x ^{2}}{b ^{2}} = 1

\frac{( y - 5 ) ^{2}}{25} - \frac{( x + 5 ) ^{2}}{9} = 1

4 x^{2} - 9 y^{2} + 4 x + 36 y - 36 = 0