What is (x^2+2x-2y^2)=0 ?

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

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(x^2+2x-2y^2)=0

(x^{2} + 2 x - 2 y^{2}) = 0

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

Solution steps

(x^{2} + 2 x - 2 y^{2}) = 0

Rewrite

(x^{2} + 2 x - 2 y^{2}) = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( x - 4 ) ^{2}}{25} - \frac{( y + 8 ) ^{2}}{49} = 1

\frac{( x - 4 ) ^{2}}{9} - \frac{( y + 5 ) ^{2}}{16} = 1

(y - 4)^{2} - \frac{( x + 1 ) ^{2}}{16} = 1

144 y^{2} - 25 x^{2} = 3600

x^{2} - 25 y^{2} - 4 x + 75 y - 27 = 0

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