What is x+y^2-x^2=10 ?

The solution to x+y^2-x^2=10 is Hyperbola with (h,k)=(1/2 ,0),a=(sqrt(39))/2 ,b=(sqrt(39))/2

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x+y^2-x^2=10

x + y^{2} - x^{2} = 10

(h, k) = (\frac{1}{2}, 0), a = \frac{39}{2}, b = \frac{39}{2}

Solution steps

x + y^{2} - x^{2} = 10

Rewrite

x + y^{2} - x^{2} = 10

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{39}{2} ) ^{2}} - \frac{( x - \frac{1}{2} ) ^{2}}{( \frac{39}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, 0), a = \frac{39}{2}, b = \frac{39}{2}

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

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

x^{2} = 4 + 3 y^{2}

(y - 2)^{2} - x^{2} = 1

(y + 1)^{2} = 4 + x^{2}

What is x+y^2-x^2=10 ?
The solution to x+y^2-x^2=10 is Hyperbola with (h,k)=(1/2 ,0),a=(sqrt(39))/2 ,b=(sqrt(39))/2