What is x^2-y^2+6x-4y+4=0 ?

The solution to x^2-y^2+6x-4y+4=0 is Hyperbola with (h,k)=(-3,-2),a=1,b=1

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x^2-y^2+6x-4y+4=0

x^{2} - y^{2} + 6 x - 4 y + 4 = 0

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

Solution steps

x^{2} - y^{2} + 6 x - 4 y + 4 = 0

Rewrite

x^{2} - y^{2} + 6 x - 4 y + 4 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

4 x^{2} - y^{2} + 16 x + 6 y = 9

\frac{x ^{2}}{289} - \frac{( y - 70 ) ^{2}}{1600} = 1

16 x^{2} - 9 y^{2} - 64 x - 54 y - 161 = 0

25 x^{2} - 4 y^{2} - 100 = 0

y^{2} = x^{2} + 529

What is x^2-y^2+6x-4y+4=0 ?
The solution to x^2-y^2+6x-4y+4=0 is Hyperbola with (h,k)=(-3,-2),a=1,b=1