What is 4x^2-25y^2-4x+10y-100=0 ?

The solution to 4x^2-25y^2-4x+10y-100=0 is Hyperbola with (h,k)=(1/2 , 1/5),a=5,b=2

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4x^2-25y^2-4x+10y-100=0

4 x^{2} - 25 y^{2} - 4 x + 10 y - 100 = 0

(h, k) = (\frac{1}{2}, \frac{1}{5}), a = 5, b = 2

Solution steps

4 x^{2} - 25 y^{2} - 4 x + 10 y - 100 = 0

Rewrite

4 x^{2} - 25 y^{2} - 4 x + 10 y - 100 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, \frac{1}{5}), a = 5, b = 2

4 x^{2} + 16 x - 9 y^{2} + 18 y - 29 = 0

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

y^{2} - x^{2} = 3

x^{2} - y^{2} - 2 x - 8 = 0

4 x^{2} - 9 y^{2} - 36 < 0

What is 4x^2-25y^2-4x+10y-100=0 ?
The solution to 4x^2-25y^2-4x+10y-100=0 is Hyperbola with (h,k)=(1/2 , 1/5),a=5,b=2