What is x^2+x-y^2=5 ?

The solution to x^2+x-y^2=5 is Hyperbola with (h,k)=(-1/2 ,0),a=(sqrt(21))/2 ,b=(sqrt(21))/2

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x^2+x-y^2=5

x^{2} + x - y^{2} = 5

(h, k) = (- \frac{1}{2}, 0), a = \frac{21}{2}, b = \frac{21}{2}

Solution steps

x^{2} + x - y^{2} = 5

Rewrite

x^{2} + x - y^{2} = 5

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{1}{2} ) ) ^{2}}{( \frac{21}{2} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{21}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{2}, 0), a = \frac{21}{2}, b = \frac{21}{2}

(x - 8)^{2} - (y + 6)^{2} = 1

4 y^{2} - 2 x^{2} = 1

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

\frac{( x - 6 ) ^{2}}{36} - \frac{( y + 1 ) ^{2}}{25} = 1

x, (x - 0.5)^{2} + (x + 0.5)^{2} = r (x)^{2}

What is x^2+x-y^2=5 ?
The solution to x^2+x-y^2=5 is Hyperbola with (h,k)=(-1/2 ,0),a=(sqrt(21))/2 ,b=(sqrt(21))/2