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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{2 + y ^{2}} = 1

25 x^{2} + 100 x - 4 y^{2} - 16 y - 16 = 0

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

x^{2} - y^{2} = 5 y

x^{2} - y^{2} = 56

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