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

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

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

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

(h, k) = (0, - 3), a = 3, b = 3

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, - 3), a = 3, b = 3

20 (x - y) = 5 x^{2} - 4 y^{2}

\frac{y ^{2}}{5} - \frac{x ^{2}}{25} = 1

\frac{x ^{2} + 1}{4} - \frac{y ^{2} - 2}{9} = - 1

36 x^{2} - 9 y^{2} + 216 x + 36 y = - 207

- 4 x^{2} + y^{2} + 8 x - 20 = 0

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