What is 9x^{(2)}-4y^{(2)}+18x-27=0 ?

The solution to 9x^{(2)}-4y^{(2)}+18x-27=0 is Hyperbola with (h,k)=(-1,0),a=2,b=3

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9x^{(2)}-4y^{(2)}+18x-27=0

9 x^{(2)} - 4 y^{(2)} + 18 x - 27 = 0

(h, k) = (- 1, 0), a = 2, b = 3

Solution steps

9 x^{2} - 4 y^{2} + 18 x - 27 = 0

Rewrite

9 x^{2} - 4 y^{2} + 18 x - 27 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 0), a = 2, b = 3

4 x^{2} - 5 y^{2} - 16 x - 30 y - 9 = 0

\frac{( x - 1.6 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{2} = 1

\frac{( x - 4 ) ^{2}}{144} - \frac{( y - 11 ) ^{2}}{25} = 1

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

7 x^{2} - 5 y^{2} - 14 x + 40 y - 108 = 0

What is 9x^{(2)}-4y^{(2)}+18x-27=0 ?
The solution to 9x^{(2)}-4y^{(2)}+18x-27=0 is Hyperbola with (h,k)=(-1,0),a=2,b=3