What is y^2+C=((3x^2)/2-6x+C) ?

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

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y^2+C=((3x^2)/2-6x+C)

y^{2} + C = (\frac{3 x ^{2}}{2} - 6 x + C)

(h, k) = (2, 0), a = 2, b = 6

Solution steps

y^{2} + C = (\frac{3 x ^{2}}{2} - 6 x + C)

Rewrite

y^{2} + C - \frac{3 x ^{2}}{2} + 6 x - C = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, 0), a = 2, b = 6

16 x^{2} - 25 y^{2} - 160 x = 0

x^{2} - 4 y^{2} - 36 = 0

y^{2} - 9 x^{2} - 6 y + 54 x = 153

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

4 x^{2} - y^{2} - 24 x - 6 y + 11 = 0

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