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

f (x) f (x) = x^{2} - x + 1

- 9 x^{2} + 4 y^{2} - 108 x + 32 y - 296 = 0

\frac{( x - 1 ) ^{2}}{9} - \frac{y ^{2}}{5} = 100

x^{2} = 2 y^{2} - 2 \cdot 0.01

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

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