What is x^2-y^2-6x-4y+7=0 ?

The solution to x^2-y^2-6x-4y+7=0 is Hyperbola with (h,k)=(3,-2),a=sqrt(2),b=sqrt(2)

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x^2-y^2-6x-4y+7=0

x^{2} - y^{2} - 6 x - 4 y + 7 = 0

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

Solution steps

x^{2} - y^{2} - 6 x - 4 y + 7 = 0

Rewrite

x^{2} - y^{2} - 6 x - 4 y + 7 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

3 x^{2} + 2 x + 92 = 3 y^{2}

4 x^{2} - 4 y^{2} = 64

y^{2} + 2 = 7 x^{2}

4 x^{2} - 25 y^{2} + 48 x + 150 y - 181 = 0

\frac{( x + 6 ) ^{2}}{32} - \frac{( y - 0.25 ) ^{2}}{100} = 1

What is x^2-y^2-6x-4y+7=0 ?
The solution to x^2-y^2-6x-4y+7=0 is Hyperbola with (h,k)=(3,-2),a=sqrt(2),b=sqrt(2)