What is 9x^2-9y^2-6x+24y=19 ?

The solution to 9x^2-9y^2-6x+24y=19 is Hyperbola with (h,k)=(1/3 , 4/3),a= 2/3 ,b= 2/3

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9x^2-9y^2-6x+24y=19

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

(h, k) = (\frac{1}{3}, \frac{4}{3}), a = \frac{2}{3}, b = \frac{2}{3}

Solution steps

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

Rewrite

9 x^{2} - 9 y^{2} - 6 x + 24 y = 19

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{3}, \frac{4}{3}), a = \frac{2}{3}, b = \frac{2}{3}

\frac{y ^{2}}{56} - \frac{x ^{2}}{56} = 1

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{4} = 1

4 (y - 4)^{2} - (x - 2)^{2} = 36

\frac{( x - 3 ) ^{2}}{16 + ( y + 5 ) ^{2}} = 1

x^{2} - y^{2} = 71

What is 9x^2-9y^2-6x+24y=19 ?
The solution to 9x^2-9y^2-6x+24y=19 is Hyperbola with (h,k)=(1/3 , 4/3),a= 2/3 ,b= 2/3