What is 9x^2-4y^2-40y-136=0 ?

The solution to 9x^2-4y^2-40y-136=0 is Hyperbola with (h,k)=(0,-5),a=2,b=3

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9x^2-4y^2-40y-136=0

9 x^{2} - 4 y^{2} - 40 y - 136 = 0

(h, k) = (0, - 5), a = 2, b = 3

Solution steps

9 x^{2} - 4 y^{2} - 40 y - 136 = 0

Rewrite

9 x^{2} - 4 y^{2} - 40 y - 136 = 0

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} - \frac{( y - ( - 5 ) ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 5), a = 2, b = 3

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

\frac{y ^{2}}{64} - \frac{x ^{2}}{9} = 1

x^{2} - y^{2} = 105

x^{2} - y^{2} - (- 10) = 0

\frac{( x - 2 ) ^{2}}{16} - \frac{( y - 4 ) ^{2}}{9} = 1

What is 9x^2-4y^2-40y-136=0 ?
The solution to 9x^2-4y^2-40y-136=0 is Hyperbola with (h,k)=(0,-5),a=2,b=3