What is y^2+7=x^2-8 ?

The solution to y^2+7=x^2-8 is Hyperbola with (h,k)=(0,0),a=sqrt(15),b=sqrt(15)

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y^2+7=x^2-8

y^{2} + 7 = x^{2} - 8

(h, k) = (0, 0), a = 15, b = 15

Solution steps

y^{2} + 7 = x^{2} - 8

Rewrite

y^{2} + 7 - x^{2} + 8 = 0

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( 15 ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 15 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 15, b = 15

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

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

What is y^2+7=x^2-8 ?
The solution to y^2+7=x^2-8 is Hyperbola with (h,k)=(0,0),a=sqrt(15),b=sqrt(15)