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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

25 x^{2} + 10918 x - 25 y^{2} - 29 y = 2321

100 x^{2} + 112952 x - 100 y^{2} - 106 y = 48838

\frac{( x + 2 ) ^{2}}{25} - \frac{( y - 1 ) ^{2}}{144} = 1

9 x^{2} - 4 y^{2} + 18 x - 24 y + 9 = 0

x^{2} - y^{2} + 8 x - 2 y + 14 = 0

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