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

The solution to y^2=(x-2)^2-1 is Hyperbola with (h,k)=(2,0),a=1,b=1

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

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

(h, k) = (2, 0), a = 1, b = 1

Solution steps

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

Rewrite

y^{2} - (x - 2)^{2} + 1 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{1 ^{2}} - \frac{( x - 2 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 0), a = 1, b = 1

y^{2} - x^{2} = 100

y^{2} - x^{2} + 5 x - 4 y + 3 = 0

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

2 x^{2} - 3 y^{2} - 12 x - 24 y + 60 = 0

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

What is y^2=(x-2)^2-1 ?
The solution to y^2=(x-2)^2-1 is Hyperbola with (h,k)=(2,0),a=1,b=1