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

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

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(x-1)^2-((y-2)^2)/3 =1

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 4 y^{2} = 9

16 y^{2} - 9 x^{2} + 54 x + 64 y - 161 = 0

9 x^{2} - 4 y^{2} - 36 > 0

16 x^{2} - 9 y^{2} - 256 y + 180 x - 452 = 0

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{25} = 1

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