What is ((x+3)^2)/4-((y-2)^2)/2 =2 ?

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

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((x+3)^2)/4-((y-2)^2)/2 =2

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

(h, k) = (- 3, 2), a = 22, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, 2), a = 22, b = 2

x^{2} - 4 y^{2} + 16 = 0

9 x^{2} - 54 x + 9 - 4 y^{2} - 8 y - 113 = 0

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

\frac{x ^{2}}{12} - \frac{y ^{2}}{16} = 1

244 - 98 y + 324 x - 49 y^{2} + 81 x^{2} = 0

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