What is ((y+2)^2)/2-((x+1)^2)/2 =1 ?

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

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((y+2)^2)/2-((x+1)^2)/2 =1

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

(h, k) = (- 1, - 2), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, - 2), a = 2, b = 2

(x - 3)^{2} - (y - 2)^{2} = 3

3 x^{2} - 5 y^{2} = 18

x^{2} - y^{2} - 6 x - 8 y + 9 = 0

x^{2} - 3 x + 2 y - y^{2} = 1

9 x^{2} - 6 y^{2} - 108 x + 128 y + 212 = 0

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