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

The solution to x^2-y^2+6x+2y=6 is Hyperbola with (h,k)=(-3,1),a=sqrt(14),b=sqrt(14)

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

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

(h, k) = (- 3, 1), a = 14, b = 14

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - ( - 3 ) ) ^{2}}{( 14 ) ^{2}} - \frac{( y - 1 ) ^{2}}{( 14 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 1), a = 14, b = 14

3 x^{2} - y^{2} + 18 x + 8 y + 38 = 0

0 = 1 + y^{2} - x^{2}

y^{2} = x^{2} + 12 x + 32

- \frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{7} = 1

(x - 2 \cdot y) \cdot (x + 2 \cdot y) = 90005

What is x^2-y^2+6x+2y=6 ?
The solution to x^2-y^2+6x+2y=6 is Hyperbola with (h,k)=(-3,1),a=sqrt(14),b=sqrt(14)