What is 9x^2-4y^2-54x-40y-55=0 ?

The solution to 9x^2-4y^2-54x-40y-55=0 is Hyperbola with (h,k)=(3,-5),a=2,b=3

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9x^2-4y^2-54x-40y-55=0

9 x^{2} - 4 y^{2} - 54 x - 40 y - 55 = 0

(h, k) = (3, - 5), a = 2, b = 3

Solution steps

9 x^{2} - 4 y^{2} - 54 x - 40 y - 55 = 0

Rewrite

9 x^{2} - 4 y^{2} - 54 x - 40 y - 55 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 5), a = 2, b = 3

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

\frac{( y - 1 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{16} = 1

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

x + x^{2} = y^{2} - 4

9 x^{2} + 36 x - 8 y^{2} + 64 y = 164

What is 9x^2-4y^2-54x-40y-55=0 ?
The solution to 9x^2-4y^2-54x-40y-55=0 is Hyperbola with (h,k)=(3,-5),a=2,b=3