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

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

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

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

(h, k) = (3, 0), a = 4, b = 4

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{4 ^{2}} - \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 0), a = 4, b = 4

y^{2} = 4 + x^{2}

\frac{( x + 1 ) ^{2}}{9} - \frac{( y - 4 ) ^{2}}{49} = 1

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

\frac{( x - 2 ) ^{2}}{81} - \frac{y ^{2}}{49} = 1

3 x^{2} - 2 y^{2} + 32 y - 134 = 0

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