What is 9y^2-25x^2-100x-108y-1=0 ?

The solution to 9y^2-25x^2-100x-108y-1=0 is Hyperbola with (h,k)=(-2,6),a=5,b=3

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9y^2-25x^2-100x-108y-1=0

9 y^{2} - 25 x^{2} - 100 x - 108 y - 1 = 0

(h, k) = (- 2, 6), a = 5, b = 3

Solution steps

9 y^{2} - 25 x^{2} - 100 x - 108 y - 1 = 0

Rewrite

9 y^{2} - 25 x^{2} - 100 x - 108 y - 1 = 0

in the form of a standard hyperbola equation

\frac{( y - 6 ) ^{2}}{5 ^{2}} - \frac{( x - ( - 2 ) ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, 6), a = 5, b = 3

\frac{x ^{2}}{6} - \frac{y ^{2}}{25} = 1

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

4 x^{2} - y^{2} - 16 x + 2 y + 3 = 0

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

x^{2} - y^{2} - 3 x + 5 y - 16 = 0

What is 9y^2-25x^2-100x-108y-1=0 ?
The solution to 9y^2-25x^2-100x-108y-1=0 is Hyperbola with (h,k)=(-2,6),a=5,b=3