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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

2 x^{2} - y^{2} + 12 x + 8 y + 6 = 0

36 + y^{2} - z^{2} = 4

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

9 x^{{2}} - 4 y^{{2}} = 36

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