What is -9x^2+25y^2-100y-125=0 ?

The solution to -9x^2+25y^2-100y-125=0 is Hyperbola with (h,k)=(0,2),a=3,b=5

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-9x^2+25y^2-100y-125=0

- 9 x^{2} + 25 y^{2} - 100 y - 125 = 0

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

Solution steps

- 9 x^{2} + 25 y^{2} - 100 y - 125 = 0

Rewrite

- 9 x^{2} + 25 y^{2} - 100 y - 125 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{11} = 1

4 x^{2} - 9 y^{2} + 32 x + 36 y + 64 = 0

4 y^{2} - x^{2} - 12 y - 16 x + 16 = 0

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

y^{2} - x^{2} = 9

What is -9x^2+25y^2-100y-125=0 ?
The solution to -9x^2+25y^2-100y-125=0 is Hyperbola with (h,k)=(0,2),a=3,b=5