What is x^2+x+41=y^2 ?

The solution to x^2+x+41=y^2 is Hyperbola with (h,k)=(-1/2 ,0),a=(sqrt(163))/2 ,b=(sqrt(163))/2

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x^2+x+41=y^2

x^{2} + x + 41 = y^{2}

(h, k) = (- \frac{1}{2}, 0), a = \frac{163}{2}, b = \frac{163}{2}

Solution steps

x^{2} + x + 41 = y^{2}

Rewrite

x^{2} + x + 41 = y^{2}

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{163}{2} ) ^{2}} - \frac{( x - ( - \frac{1}{2} ) ) ^{2}}{( \frac{163}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{2}, 0), a = \frac{163}{2}, b = \frac{163}{2}

x^{2} + 10 x + 25 - y^{2} - 6 y + 9 = 36

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

\frac{x ^{2}}{64} - \frac{y ^{2}}{9} = 1

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

36 y^{2} - x^{2} = 9

What is x^2+x+41=y^2 ?
The solution to x^2+x+41=y^2 is Hyperbola with (h,k)=(-1/2 ,0),a=(sqrt(163))/2 ,b=(sqrt(163))/2