What is (x-5)^2-(y-4)^2=1 ?

The solution to (x-5)^2-(y-4)^2=1 is Hyperbola with (h,k)=(5,4),a=1,b=1

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(x-5)^2-(y-4)^2=1

(x - 5)^{2} - (y - 4)^{2} = 1

(h, k) = (5, 4), a = 1, b = 1

Solution steps

(x - 5)^{2} - (y - 4)^{2} = 1

Rewrite

(x - 5)^{2} - (y - 4)^{2} = 1

in the form of a standard hyperbola equation

\frac{( x - 5 ) ^{2}}{1 ^{2}} - \frac{( y - 4 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (5, 4), a = 1, b = 1

144 x^{2} - 25 y^{2} + 864 x - 100 y - 2404 = 0

25 x^{2} - 16 y^{2} + 50 x + 128 y - 631 = 0

4 x^{2} - 4 y^{2} = 16

2 x^{2} - 3 y^{2} = 30

\frac{20}{x + y} + \frac{12}{x - y} = 5

What is (x-5)^2-(y-4)^2=1 ?
The solution to (x-5)^2-(y-4)^2=1 is Hyperbola with (h,k)=(5,4),a=1,b=1