What is the answer to solvefor y,xy-y=sqrt(x^2+y^2) ?

The answer to solvefor y,xy-y=sqrt(x^2+y^2) is y=sqrt(x/(x-2)) {x=0},y=-sqrt(x/(x-2)) {x<= 0}

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solvefor y,xy-y=sqrt(x^2+y^2)

solve for

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

y = \frac{x}{x - 2} {x = 0}, y = - \frac{x}{x - 2} {x \leq 0}

Solution steps

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

Square both sides:

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

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

Solve

y^{2} x^{2} - 2 y^{2} x + y^{2} = x^{2} + y^{2} : y = \frac{x}{x - 2}, y = - \frac{x}{x - 2}

y = \frac{x}{x - 2}, y = - \frac{x}{x - 2}

Verify Solutions:

y = \frac{x}{x - 2} {x = 0}, y = - \frac{x}{x - 2} {x \leq 0}

The solutions are

y = \frac{x}{x - 2} {x = 0}, y = - \frac{x}{x - 2} {x \leq 0}

3 3 x - 2 = - 5

1 - 2 x - 13 + x = x + 4

- 1 - x + 6 = 6

3 x - 15 - 13 = - 10

1 - x^{\frac{2}{3}} = 0

What is the answer to solvefor y,xy-y=sqrt(x^2+y^2) ?
The answer to solvefor y,xy-y=sqrt(x^2+y^2) is y=sqrt(x/(x-2)) {x=0},y=-sqrt(x/(x-2)) {x<= 0}