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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

4 x^{2} - 9 y^{2} + 8 x - 36 y = 0

(\frac{x ^{2}}{1} + \frac{y ^{2}}{1 - 16}) (1 - 16) = 1 (1 - 16)

\frac{x ^{2}}{25} - \frac{y ^{2}}{81} = 1

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

\frac{( y - 3 ) ^{2}}{49} - \frac{( x + 2 ) ^{2}}{16} = 1

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