What is 4y^2-9x^2+8y-54x-81=0 ?

The solution to 4y^2-9x^2+8y-54x-81=0 is Hyperbola with (h,k)=(-3,-1),a=1,b= 2/3

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4y^2-9x^2+8y-54x-81=0

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

4 y^{2} - x^{2} - 8 y - 4 x - 4 = 0

(y + 2)^{2} - x^{2} = 8

16 x^{2} - 9 y^{2} + 576 = 0

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

x^{2} - y^{2} - 100 = 0

What is 4y^2-9x^2+8y-54x-81=0 ?
The solution to 4y^2-9x^2+8y-54x-81=0 is Hyperbola with (h,k)=(-3,-1),a=1,b= 2/3