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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(y + 1)^{2} = 4 + x^{2}

\frac{( x + 4 ) ^{2}}{36} - \frac{( y - 2 ) ^{2}}{16} = 1

- 64 x^{2} + 25 y^{2} - 1152 x - 350 y - 5559 = 0

5 y^{(2)} - 16 x^{(2)} - 400 = 0

x^{2} - y^{2} + 7 x + 8 y - 5 = 0

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