What is 2y^2+10/2 x^2-8+1=3y^2-4 ?

The solution to 2y^2+10/2 x^2-8+1=3y^2-4 is Hyperbola with (h,k)=(0,0),a=sqrt(3/5),b=sqrt(3)

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2y^2+10/2 x^2-8+1=3y^2-4

2 y^{2} + \frac{10}{2} x^{2} - 8 + 1 = 3 y^{2} - 4

(h, k) = (0, 0), a = \frac{3}{5}, b = 3

Solution steps

2 y^{2} + \frac{10}{2} x^{2} - 8 + 1 = 3 y^{2} - 4

Rewrite

2 y^{2} + \frac{10}{2} x^{2} - 8 + 1 - 3 y^{2} + 4 = 0

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{3}{5} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{3}{5}, b = 3

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

13 x^{2} - 14 x - 26 = 13 y^{2} + 18 y - 7

19 x^{2} - 9 y^{2} - 64 x - 18 y + 199 = 0

a^{2} - b^{2} = 396

\frac{x ^{2}}{140} - \frac{( y - 6 ) ^{2}}{4} = - 1

What is 2y^2+10/2 x^2-8+1=3y^2-4 ?
The solution to 2y^2+10/2 x^2-8+1=3y^2-4 is Hyperbola with (h,k)=(0,0),a=sqrt(3/5),b=sqrt(3)