What is y^2-9x^2-8y-54x-81=0 ?

The solution to y^2-9x^2-8y-54x-81=0 is Hyperbola with (h,k)=(-3,4),a=4,b= 4/3

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y^2-9x^2-8y-54x-81=0

y^{2} - 9 x^{2} - 8 y - 54 x - 81 = 0

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

Solution steps

y^{2} - 9 x^{2} - 8 y - 54 x - 81 = 0

Rewrite

y^{2} - 9 x^{2} - 8 y - 54 x - 81 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

4 x^{2} - 12 y^{2} - 24 x + 24 y + 51 = 0

y = \frac{273 x}{340 y} x + \frac{240000}{340}

\frac{y ^{2}}{4} - \frac{x ^{2}}{12} = 1

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

\frac{( x - 27 ) ^{2}}{6} - \frac{( y - 4 ) ^{2}}{10} = 1

What is y^2-9x^2-8y-54x-81=0 ?
The solution to y^2-9x^2-8y-54x-81=0 is Hyperbola with (h,k)=(-3,4),a=4,b= 4/3