What is 4x^2-25y^2-50y-125=0 ?

The solution to 4x^2-25y^2-50y-125=0 is Hyperbola with (h,k)=(0,-1),a=5,b=2

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4x^2-25y^2-50y-125=0

4 x^{2} - 25 y^{2} - 50 y - 125 = 0

(h, k) = (0, - 1), a = 5, b = 2

Solution steps

4 x^{2} - 25 y^{2} - 50 y - 125 = 0

Rewrite

4 x^{2} - 25 y^{2} - 50 y - 125 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 5, b = 2

9 x^{2} - 16 y^{2} - 54 x - 64 y + 1 = 0

x^{2} - 4 y^{2} - 4 x + 24 y + 37 = 0

6 x^{2} - y^{2} - 12 x - 6 y + 5 = 0

4 a 2 - 9 b 2 = (2 a 2 + 3 b 2) (2 a 2 - 3 b 2)

25 x^{2} - 9 y^{2} + 50 x - 36 y - 236 = 0

What is 4x^2-25y^2-50y-125=0 ?
The solution to 4x^2-25y^2-50y-125=0 is Hyperbola with (h,k)=(0,-1),a=5,b=2