2x^2-4y^2+9x-15y-18=0

Lösung

2 x^{2} - 4 y^{2} + 9 x - 15 y - 18 = 0

(h, k) = (- \frac{9}{4}, - \frac{15}{8}), a = \frac{15}{4 2}, b = \frac{15}{8}

Schritte zur Lösung

2 x^{2} - 4 y^{2} + 9 x - 15 y - 18 = 0

Rewrite

2 x^{2} - 4 y^{2} + 9 x - 15 y - 18 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{9}{4} ) ) ^{2}}{( \frac{15}{4 2} ) ^{2}} - \frac{( y - ( - \frac{15}{8} ) ) ^{2}}{( \frac{15}{8} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{9}{4}, - \frac{15}{8}), a = \frac{15}{4 2}, b = \frac{15}{8}

4 x^{2} - 32 x - y^{2} - 4 y + 24 = 0

(x - 2)^{2} - (y - 4)^{2} = 81

x^{2} - 9 y^{2} - 2 x + 54 y - 116 = 0

9 x^{2} - 4 y^{2} - 18 x + 24 y + 45 = 0

\frac{y ^{2}}{25} - \frac{( x - 4 ) ^{2}}{16} = 1