What is y/3 =(x^2)/(2+y) ?

The solution to y/3 =(x^2)/(2+y) is Hyperbola with (h,k)=(0,-1),a=1,b=sqrt(1/3)

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y/3 =(x^2)/(2+y)

\frac{y}{3} = \frac{x ^{2}}{2 + y}

(h, k) = (0, - 1), a = 1, b = \frac{1}{3}

Solution steps

\frac{y}{3} = \frac{x ^{2}}{2 + y}

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 1, b = \frac{1}{3}

5 y^{2} - 4 x^{2} - 20 = 0

\frac{x ^{2}}{81} - \frac{y ^{2}}{49} = 1

x^{2} - 4 y^{2} + 2 x - 16 y - 4 = 0

(a + b) \cdot (a - b) = 20

y^{2} - 2 x^{2} + 6 y - 16 x - 31 = 0

What is y/3 =(x^2)/(2+y) ?
The solution to y/3 =(x^2)/(2+y) is Hyperbola with (h,k)=(0,-1),a=1,b=sqrt(1/3)