What is -9x^2+25y^2+50y-200=0 ?

The solution to -9x^2+25y^2+50y-200=0 is Hyperbola with (h,k)=(0,-1),a=3,b=5

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-9x^2+25y^2+50y-200=0

- 9 x^{2} + 25 y^{2} + 50 y - 200 = 0

(h, k) = (0, - 1), a = 3, b = 5

Solution steps

- 9 x^{2} + 25 y^{2} + 50 y - 200 = 0

Rewrite

- 9 x^{2} + 25 y^{2} + 50 y - 200 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 3, b = 5

4 x^{2} - 9 y^{2} - 144 = 0

16 y^{2} - 9 x^{2} + 54 + 64 y - 161 = 0

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

y^{2} - 36 x^{2} = 36

12 x^{2} + 6 y^{2} + 3 = 10 x^{2} + 10 y^{2} + 4

What is -9x^2+25y^2+50y-200=0 ?
The solution to -9x^2+25y^2+50y-200=0 is Hyperbola with (h,k)=(0,-1),a=3,b=5