What is ((y-1)/4)^2-((x-3)/9)^2=1 ?

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

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((y-1)/4)^2-((x-3)/9)^2=1

(\frac{y - 1}{4})^{2} - (\frac{x - 3}{9})^{2} = 1

(h, k) = (3, 1), a = 4, b = 9

Solution steps

(\frac{y - 1}{4})^{2} - (\frac{x - 3}{9})^{2} = 1

Rewrite

(\frac{y - 1}{4})^{2} - (\frac{x - 3}{9})^{2} = 1

in the form of a standard hyperbola equation

\frac{( y - 1 ) ^{2}}{4 ^{2}} - \frac{( x - 3 ) ^{2}}{9 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 1), a = 4, b = 9

4 x^{2} - 9 y^{2} + 144 = 0

- 4 x^{2} + 5 y^{2} + 21 x - 5 y + 28 = 0

4 (x - 4)^{2} - 25 (y - 1)^{2} = 100

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

143 x^{2} - y^{2} + 152 x + 2 y + 164 = 0

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