What is 2500x^2-640x+41=y^2 ?

The solution to 2500x^2-640x+41=y^2 is Hyperbola with (h,k)=(16/125 ,0),a= 1/5 ,b= 1/250

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2500x^2-640x+41=y^2

2500 x^{2} - 640 x + 41 = y^{2}

(h, k) = (\frac{16}{125}, 0), a = \frac{1}{5}, b = \frac{1}{250}

Solution steps

2500 x^{2} - 640 x + 41 = y^{2}

Rewrite

2500 x^{2} - 640 x + 41 = y^{2}

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{1}{5} ) ^{2}} - \frac{( x - \frac{16}{125} ) ^{2}}{( \frac{1}{250} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{16}{125}, 0), a = \frac{1}{5}, b = \frac{1}{250}

5 x^{2} - 3 y^{2} + 31 x + 23 y + 24 = 0

y^{2} = \frac{( 900 + 36 ( x - 8 ) ^{2} )}{25}

\frac{x ^{2}}{400} - \frac{y ^{2}}{625} = 1

3 x^{2} - 9 y^{2} - 18 x + 18 y - 54 = 0

p^{2} = 32 + q^{2}

What is 2500x^2-640x+41=y^2 ?
The solution to 2500x^2-640x+41=y^2 is Hyperbola with (h,k)=(16/125 ,0),a= 1/5 ,b= 1/250