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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y^{2} = (- x)^{2} + 6

\frac{4 b - 4 a}{b - a} = (a^{2} - b^{2})

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

\frac{( x - 3 ) ^{2}}{49} - \frac{( y + 5 ) ^{2}}{25} = 1

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

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