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

The solution to y^2=(x-4)^2-1 is Hyperbola with (h,k)=(4,0),a=1,b=1

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

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

(h, k) = (4, 0), a = 1, b = 1

Solution steps

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

Rewrite

y^{2} - (x - 4)^{2} + 1 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{1 ^{2}} - \frac{( x - 4 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, 0), a = 1, b = 1

\frac{( x + 5 ) ^{2}}{64} - \frac{( y - 1 ) ^{2}}{36} = 1

3 x^{2} - 3 y^{2} = 2 y

16 x^{2} - 9 y^{2} - 90 y - 369 = 0

y^{2} - z^{2} + 2 z - 4 = 0

9 x^{2} - 4 y^{2} - 54 x + 8 y - 113 = 0

What is y^2=(x-4)^2-1 ?
The solution to y^2=(x-4)^2-1 is Hyperbola with (h,k)=(4,0),a=1,b=1