What is 9x^2-4y^2+18x+32y=119 ?

The solution to 9x^2-4y^2+18x+32y=119 is Hyperbola with (h,k)=(-1,4),a= 8/3 ,b=4

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9x^2-4y^2+18x+32y=119

9 x^{2} - 4 y^{2} + 18 x + 32 y = 119

(h, k) = (- 1, 4), a = \frac{8}{3}, b = 4

Solution steps

9 x^{2} - 4 y^{2} + 18 x + 32 y = 119

Rewrite

9 x^{2} - 4 y^{2} + 18 x + 32 y = 119

in the form of a standard hyperbola equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{8}{3} ) ^{2}} - \frac{( y - 4 ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, 4), a = \frac{8}{3}, b = 4

3 x^{2} - 3 y^{2} + 30 x - 6 y + 25 = 0

\frac{( x - 7 ) ^{2}}{a ^{2}} - \frac{( y + 6 ) ^{2}}{b ^{2}} = 1

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

\frac{( y + 2 ) ^{2}}{36} - x^{2} = 1

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

What is 9x^2-4y^2+18x+32y=119 ?
The solution to 9x^2-4y^2+18x+32y=119 is Hyperbola with (h,k)=(-1,4),a= 8/3 ,b=4