What is (x-2)^2-(y+3)^2=12 ?

The solution to (x-2)^2-(y+3)^2=12 is Hyperbola with (h,k)=(2,-3),a=2sqrt(3),b=2sqrt(3)

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(x-2)^2-(y+3)^2=12

(x - 2)^{2} - (y + 3)^{2} = 12

(h, k) = (2, - 3), a = 23, b = 23

Solution steps

(x - 2)^{2} - (y + 3)^{2} = 12

Rewrite

(x - 2)^{2} - (y + 3)^{2} = 12

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (2, - 3), a = 23, b = 23

4 x^{2} - y^{2} + 12 x + 5 = 0

y^{2} - x^{2} = \frac{1}{25}

x^{2} - 2 y^{2} - 2 x + 8 y + 5 = 0

12 x^{2} - 4 y^{2} = 96

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

What is (x-2)^2-(y+3)^2=12 ?
The solution to (x-2)^2-(y+3)^2=12 is Hyperbola with (h,k)=(2,-3),a=2sqrt(3),b=2sqrt(3)