(40)/(x+y)+2/(x-y)=5

Lösung

\frac{40}{x + y} + \frac{2}{x - y} = 5

(h, k) = (\frac{21}{5}, \frac{19}{5}), a = \frac{4}{5}, b = \frac{4}{5}

Schritte zur Lösung

\frac{40}{x + y} + \frac{2}{x - y} = 5

Rewrite

\frac{40}{x + y} + \frac{2}{x - y} = 5

in the form of a standard hyperbola equation

\frac{( x - \frac{21}{5} ) ^{2}}{( \frac{4}{5} ) ^{2}} - \frac{( y - \frac{19}{5} ) ^{2}}{( \frac{4}{5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{21}{5}, \frac{19}{5}), a = \frac{4}{5}, b = \frac{4}{5}

\frac{( y - 5 ) ^{2}}{15} - \frac{( x + 4 ) ^{2}}{49} = 1

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

4 x^{2} - 9 y^{2} + 8 x + 36 y - 68 = 0

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

3 x^{2} - 12 x - \frac{y ^{2}}{4} - \frac{y}{2} + \frac{43}{4} = 0