What is y/(2x+y^2)= x/((4+xy)) ?

The solution to y/(2x+y^2)= x/((4+xy)) is Parabola with (h,k)=(0,0),p= 1/2

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y/(2x+y^2)= x/((4+xy))

\frac{y}{2 x + y ^{2}} = \frac{x}{( 4 + x y )}

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

Solution steps

\frac{y}{2 x + y ^{2}} = \frac{x}{4 + x y}

Rewrite

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

in the standard form

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

Therefore parabola properties are:

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

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

2 x^{2} + 12 x + 14 - 14 y = 0

(x - 4)^{2} = - 6 (y + 8)

x^{2} + 5 x + 6 = 0.5 u (y)

x = \frac{1}{9} y^{2}

What is y/(2x+y^2)= x/((4+xy)) ?
The solution to y/(2x+y^2)= x/((4+xy)) is Parabola with (h,k)=(0,0),p= 1/2