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The slope of the tangent  −2x/y

that is  dy/dx = -2x/y    
         ydy   = -2xdx
         
itegrating both the side
          
          y^2/2  = -2*x^2/2 + c
          
          y^2/2 + x^2 = c
          
          it is in the form of x^2 / a^2 + y^2 / b^2 =c
          
          so the curve is an ellipse with a =1 and b = √2.

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