What is (x-5)^2-(y-4)^2=25 ?

The solution to (x-5)^2-(y-4)^2=25 is Hyperbola with (h,k)=(5,4),a=5,b=5

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(x-5)^2-(y-4)^2=25

(x - 5)^{2} - (y - 4)^{2} = 25

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

Solution steps

(x - 5)^{2} - (y - 4)^{2} = 25

Rewrite

(x - 5)^{2} - (y - 4)^{2} = 25

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 3 y^{2} = 4

x^{2} - y^{2} = - 7

x^{2} - y^{2} = - 8

6 x^{2} - 8 y^{2} - 108 x - 64 y = - 310

\frac{( a - b )}{a ^{2} - 2 ab + b ^{2}} - \frac{3}{a - b} = a + b

What is (x-5)^2-(y-4)^2=25 ?
The solution to (x-5)^2-(y-4)^2=25 is Hyperbola with (h,k)=(5,4),a=5,b=5