What is 9x^2-25y^2-90x-100y-100=0 ?

The solution to 9x^2-25y^2-90x-100y-100=0 is Hyperbola with (h,k)=(5,-2),a=5,b=3

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9x^2-25y^2-90x-100y-100=0

9 x^{2} - 25 y^{2} - 90 x - 100 y - 100 = 0

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

Solution steps

9 x^{2} - 25 y^{2} - 90 x - 100 y - 100 = 0

Rewrite

9 x^{2} - 25 y^{2} - 90 x - 100 y - 100 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( y ^{2} )}{25} - \frac{( x ^{2} )}{9} = 1

4 x^{2} - 25 y^{2} + 48 + 150 - 181 = 0

9 y^{2} + 36 y - 4 x^{2} - 16 x - 16 = 0

\frac{x ^{2}}{56} - \frac{y ^{2}}{20} = 1

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

What is 9x^2-25y^2-90x-100y-100=0 ?
The solution to 9x^2-25y^2-90x-100y-100=0 is Hyperbola with (h,k)=(5,-2),a=5,b=3