What is ((a^2+b^2))/2-2(a^2-b^2)=-15 ?

The solution to ((a^2+b^2))/2-2(a^2-b^2)=-15 is Hyperbola with (h,k)=(0,0),a=sqrt(10),b=sqrt(6)

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((a^2+b^2))/2-2(a^2-b^2)=-15

\frac{( a ^{2} + b ^{2} )}{2} - 2 (a^{2} - b^{2}) = - 15

(h, k) = (0, 0), a = 10, b = 6

Solution steps

\frac{a ^{2} + b ^{2}}{2} - 2 (a^{2} - b^{2}) = - 15

Rewrite

\frac{a ^{2} + b ^{2}}{2} - 2 (a^{2} - b^{2}) = - 15

in the form of a standard hyperbola equation

\frac{( a - 0 ) ^{2}}{( 10 ) ^{2}} - \frac{( b - 0 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 10, b = 6

4 x^{2} + 8 x - y^{2} + 2 y = - 5

\frac{( y + 5 ) ^{2}}{25} - \frac{( x - 6 ) ^{2}}{16} = 1

2 x^{2} - 3 y^{2} = 15

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

(x - 9)^{2} - 9 (y + 7)^{2} = 1

What is ((a^2+b^2))/2-2(a^2-b^2)=-15 ?
The solution to ((a^2+b^2))/2-2(a^2-b^2)=-15 is Hyperbola with (h,k)=(0,0),a=sqrt(10),b=sqrt(6)