What is x^2-y^2-6x-8y+9=0 ?

The solution to x^2-y^2-6x-8y+9=0 is Hyperbola with (h,k)=(3,-4),a=4,b=4

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x^2-y^2-6x-8y+9=0

x^{2} - y^{2} - 6 x - 8 y + 9 = 0

(h, k) = (3, - 4), a = 4, b = 4

Solution steps

x^{2} - y^{2} - 6 x - 8 y + 9 = 0

Rewrite

x^{2} - y^{2} - 6 x - 8 y + 9 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 4), a = 4, b = 4

x^{2} - 3 x + 2 y - y^{2} = 1

9 x^{2} - 6 y^{2} - 108 x + 128 y + 212 = 0

\frac{Y ^{2}}{1} - \frac{X ^{2}}{16} = 1

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

16 x^{2} - y^{2} = 144

What is x^2-y^2-6x-8y+9=0 ?
The solution to x^2-y^2-6x-8y+9=0 is Hyperbola with (h,k)=(3,-4),a=4,b=4