What is x^2-y^2+6x=19 ?

The solution to x^2-y^2+6x=19 is Hyperbola with (h,k)=(-3,0),a=2sqrt(7),b=2sqrt(7)

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x^2-y^2+6x=19

x^{2} - y^{2} + 6 x = 19

(h, k) = (- 3, 0), a = 27, b = 27

Solution steps

x^{2} - y^{2} + 6 x = 19

Rewrite

x^{2} - y^{2} + 6 x = 19

in the form of a standard hyperbola equation

\frac{( x - ( - 3 ) ) ^{2}}{( 2 7 ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 2 7 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 0), a = 27, b = 27

x^{2} - y^{2} + 6 x = 11

\frac{( x - 0 ) ^{2}}{4} - \frac{( y - ( - 1 ) ) ^{2}}{16} = 1

\frac{y ^{2}}{2} + 3 y = \frac{x ^{2}}{2}

20 (x - y) = 5 x^{2} - 4 y^{2}

\frac{y ^{2}}{5} - \frac{x ^{2}}{25} = 1

What is x^2-y^2+6x=19 ?
The solution to x^2-y^2+6x=19 is Hyperbola with (h,k)=(-3,0),a=2sqrt(7),b=2sqrt(7)