What is (y/2)^2-2y= 3/2 x^2-5x ?

The solution to (y/2)^2-2y= 3/2 x^2-5x is Hyperbola with (h,k)=(5/3 ,4),a= 1/3 ,b=sqrt(2/3)

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(y/2)^2-2y= 3/2 x^2-5x

(\frac{y}{2})^{2} - 2 y = \frac{3}{2} x^{2} - 5 x

(h, k) = (\frac{5}{3}, 4), a = \frac{1}{3}, b = \frac{2}{3}

Solution steps

(\frac{y}{2})^{2} - 2 y = \frac{3}{2} x^{2} - 5 x

Rewrite

(\frac{y}{2})^{2} - 2 y - \frac{3}{2} x^{2} + 5 x = 0

in the form of a standard hyperbola equation

\frac{( x - \frac{5}{3} ) ^{2}}{( \frac{1}{3} ) ^{2}} - \frac{( y - 4 ) ^{2}}{( \frac{2}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{5}{3}, 4), a = \frac{1}{3}, b = \frac{2}{3}

x^{2} - 4 y^{2} + 6 x + 24 y - 40 = 0

\frac{( y - 1 ) ^{2}}{9} - \frac{( x + 2 ) ^{2}}{16} = 1

x^{2} - 9 y^{2} = 27

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

4 x^{2} = y^{2} + 100

What is (y/2)^2-2y= 3/2 x^2-5x ?
The solution to (y/2)^2-2y= 3/2 x^2-5x is Hyperbola with (h,k)=(5/3 ,4),a= 1/3 ,b=sqrt(2/3)