What is ((y-1)^2)/4-((x+3)^2)/9 =1 ?

The solution to ((y-1)^2)/4-((x+3)^2)/9 =1 is Hyperbola with (h,k)=(-3,1),a=2,b=3

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((y-1)^2)/4-((x+3)^2)/9 =1

\frac{( y - 1 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

(h, k) = (- 3, 1), a = 2, b = 3

Solution steps

\frac{( y - 1 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

Rewrite

\frac{( y - 1 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 3, 1), a = 2, b = 3

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

9 x^{2} + 36 x - 8 y^{2} + 64 y = 164

9 x^{2} - 16 y^{2} + 144 x + 32 y + 79 = 0

0 = y^{2} - y - \frac{x ^{2}}{4} + 24

4 x^{2} - 9 y^{2} - 16 x + 36 y + 16 = 0

What is ((y-1)^2)/4-((x+3)^2)/9 =1 ?
The solution to ((y-1)^2)/4-((x+3)^2)/9 =1 is Hyperbola with (h,k)=(-3,1),a=2,b=3