What is x+x^2=y^2-4 ?

The solution to x+x^2=y^2-4 is Hyperbola with (h,k)=(-1/2 ,0),a=(sqrt(15))/2 ,b=(sqrt(15))/2

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x+x^2=y^2-4

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

(h, k) = (- \frac{1}{2}, 0), a = \frac{15}{2}, b = \frac{15}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{15}{2} ) ^{2}} - \frac{( x - ( - \frac{1}{2} ) ) ^{2}}{( \frac{15}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{2}, 0), a = \frac{15}{2}, b = \frac{15}{2}

9 x^{2} + 36 x - 8 y^{2} + 64 y = 164

9 x^{2} - 16 y^{2} + 144 x + 32 y + 79 = 0

0 = y^{2} - y - \frac{x ^{2}}{4} + 24

4 x^{2} - 9 y^{2} - 16 x + 36 y + 16 = 0

\frac{x ^{2}}{16} - \frac{y ^{2}}{7} = 1

What is x+x^2=y^2-4 ?
The solution to x+x^2=y^2-4 is Hyperbola with (h,k)=(-1/2 ,0),a=(sqrt(15))/2 ,b=(sqrt(15))/2