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

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

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

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

(h, k) = (4, - 1), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (4, - 1), a = 2, b = 2

x^{2} + 24 = y^{2} + 6 x - 2 y

x^{2} - y^{2} + 10 x - 6 y = 2

x^{2} - y^{2} = 200 0^{2}

6 x^{2} - \frac{2}{3} y^{2} = 4

4 x^{2} - y^{2} - 2 y - 2 = 0

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