What is ((x-1)^2)/4-(y+3)^2=1 ?

The solution to ((x-1)^2)/4-(y+3)^2=1 is Hyperbola with (h,k)=(1,-3),a=2,b=1

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((x-1)^2)/4-(y+3)^2=1

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

(h, k) = (1, - 3), a = 2, b = 1

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 3), a = 2, b = 1

2 xx - 3 yy = - 1214

3 x^{2} - 6 x - 4 y^{2} = 9

9 x^{2} - 16 y^{2} = 64

\frac{x ^{2}}{25} - \frac{y ^{2}}{49} = 1

x^{2} = y^{2} - 25

What is ((x-1)^2)/4-(y+3)^2=1 ?
The solution to ((x-1)^2)/4-(y+3)^2=1 is Hyperbola with (h,k)=(1,-3),a=2,b=1