What is y 1/3 y-x^2+2x=-5 ?

The solution to y 1/3 y-x^2+2x=-5 is Hyperbola with (h,k)=(1,0),a=sqrt(6),b=3sqrt(2)

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y 1/3 y-x^2+2x=-5

y \frac{1}{3} y - x^{2} + 2 x = - 5

(h, k) = (1, 0), a = 6, b = 32

Solution steps

y \frac{1}{3} y - x^{2} + 2 x = - 5

Rewrite

y \frac{1}{3} y - x^{2} + 2 x = - 5

in the form of a standard hyperbola equation

\frac{( x - 1 ) ^{2}}{( 6 ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 3 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, 0), a = 6, b = 32

(x + 3)^{2} - (y + 2)^{2} = 9

5 (y + 3)^{2} - 4 (x - 1)^{2} = 20

\frac{( x - 3 ) ^{2}}{6} - \frac{( y - 1 ) ^{2}}{12} = 1

\frac{( y - 1 ) ^{2}}{36} - \frac{( x - 2 ) ^{2}}{64} = 1

- x^{2} + 4 y^{2} - 16 y + 12 = 0

What is y 1/3 y-x^2+2x=-5 ?
The solution to y 1/3 y-x^2+2x=-5 is Hyperbola with (h,k)=(1,0),a=sqrt(6),b=3sqrt(2)