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

The solution to x^2-6x-2y^2+7=0 is Hyperbola with (h,k)=(3,0),a=sqrt(2),b=1

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

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

(h, k) = (3, 0), a = 2, b = 1

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{( 2 ) ^{2}} - \frac{( y - 0 ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 0), a = 2, b = 1

\frac{( x - 3 ) ^{2}}{16} - \frac{( y + 1 ) ^{2}}{9} = 1

(\frac{y}{100})^{2} - \frac{x ^{2}}{49} = 1

(x + y) (x - y) = 60.49

9 x^{2} - 4 y^{2} = 144

9 x^{2} - 16 y^{2} - 54 x + 32 y - 79 = 0

What is x^2-6x-2y^2+7=0 ?
The solution to x^2-6x-2y^2+7=0 is Hyperbola with (h,k)=(3,0),a=sqrt(2),b=1