What is ((x-2)^2)/4-(y^2)/9 =1 ?

The solution to ((x-2)^2)/4-(y^2)/9 =1 is Hyperbola with (h,k)=(2,0),a=2,b=3

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((x-2)^2)/4-(y^2)/9 =1

\frac{( x - 2 ) ^{2}}{4} - \frac{y ^{2}}{9} = 1

(h, k) = (2, 0), a = 2, b = 3

Solution steps

\frac{( x - 2 ) ^{2}}{4} - \frac{y ^{2}}{9} = 1

Rewrite

\frac{( x - 2 ) ^{2}}{4} - \frac{y ^{2}}{9} = 1

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{2 ^{2}} - \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 0), a = 2, b = 3

2 a - 3 b^{2} = 4 a^{2} - 9 b^{2}

\frac{( y - 4 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1

9 x^{2} - 36 x - y^{2} - 6 y + 18 = 0

x^{2} - y^{2} - y + 9 = 0

16 x^{2} - 9 y^{2} - 96 x + 36 y - 36 = 0

What is ((x-2)^2)/4-(y^2)/9 =1 ?
The solution to ((x-2)^2)/4-(y^2)/9 =1 is Hyperbola with (h,k)=(2,0),a=2,b=3