What is x/y-y/x = 1/y ?

The solution to x/y-y/x = 1/y is Hyperbola with (h,k)=(1/2 ,0),a= 1/2 ,b= 1/2

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x/y-y/x = 1/y

\frac{x}{y} - \frac{y}{x} = \frac{1}{y}

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{1}{2}

Solution steps

\frac{x}{y} - \frac{y}{x} = \frac{1}{y}

Rewrite

\frac{x}{y} - \frac{y}{x} - \frac{1}{y} = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{1}{2} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{1}{2}

(x - y) (x + y) = 2022

\frac{( y + 1 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{16} = 1

\frac{x ^{2}}{7} - \frac{7 y ^{2}}{42} = 1

\frac{( x - 3 ) ^{2}}{64} - \frac{( y + 2 ) ^{2}}{16} = 1

\frac{x ^{2}}{36} - \frac{y ^{2}}{49} = 1

What is x/y-y/x = 1/y ?
The solution to x/y-y/x = 1/y is Hyperbola with (h,k)=(1/2 ,0),a= 1/2 ,b= 1/2