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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 0

- 4 x^{2} + 8 y^{2} + 10 x - 6 y - 8 = 0

25 x^{2} - 9 y^{2} - 200 x + 36 y + 139 = 0

- 8 x^{2} + 4 y^{2} + 10 x - 6 y - 8 = 0

\frac{( x + 2 ) ^{2}}{9} - \frac{( y - 1 ) ^{2}}{16} = 1

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