What is x^2-2x-y^2-6y+9=0 ?

The solution to x^2-2x-y^2-6y+9=0 is Hyperbola with (h,k)=(1,-3),a=sqrt(17),b=sqrt(17)

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x^2-2x-y^2-6y+9=0

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

(h, k) = (1, - 3), a = 17, b = 17

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{( 17 ) ^{2}} - \frac{( x - 1 ) ^{2}}{( 17 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, - 3), a = 17, b = 17

\frac{y ^{2}}{36} - \frac{x ^{2}}{64} = 1

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

\frac{x ^{2}}{4} - \frac{y ^{2}}{36} = 1

x^{2} + 2 y + x = 2 y^{2} + 3 y + 2 x + 2

- 4 x^{2} + 24 x + 16 y^{2} - 128 y + 156 = 0

What is x^2-2x-y^2-6y+9=0 ?
The solution to x^2-2x-y^2-6y+9=0 is Hyperbola with (h,k)=(1,-3),a=sqrt(17),b=sqrt(17)