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

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

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((x-2)^2)/4-(y-1)^2=1

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

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

36 x^{2} - y^{2} - 24 x + 6 y - 41 = 0

\frac{x ^{2}}{4} + \frac{x}{2} - \frac{y ^{2}}{9} - \frac{2 y}{9} + \frac{1}{6} = 0

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

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