What is y^2=x^2+2x-3 ?

The solution to y^2=x^2+2x-3 is Hyperbola with (h,k)=(-1,0),a=2,b=2

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y^2=x^2+2x-3

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

(h, k) = (- 1, 0), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 0), a = 2, b = 2

\frac{y ^{2}}{9} - \frac{x ^{2}}{25} = 1

\frac{x ^{2}}{9} - \frac{y ^{2}}{49} = 1

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

x^{2} - y^{2} = 40

x^{2} - 3 y^{2} + 12 = 0

What is y^2=x^2+2x-3 ?
The solution to y^2=x^2+2x-3 is Hyperbola with (h,k)=(-1,0),a=2,b=2