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

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

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

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

(h, k) = (5, 2), a = 1, b = 1

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (5, 2), a = 1, b = 1

a^{2} - b^{2} = 3000

625 y^{2} - 400 x^{2} = 250000

49 x^{2} - 25 y^{2} - 686 x - 50 y - 2375 = 0

49 x^{2} - 25 y^{2} - 686 x - 50 y - 2375 = 1

- \frac{( x - 5 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{3} = 1

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