What is y^2-y-x-3=x^2-x-y-1 ?

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

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y^2-y-x-3=x^2-x-y-1

y^{2} - y - x - 3 = x^{2} - x - y - 1

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

Solution steps

y^{2} - y - x - 3 = x^{2} - x - y - 1

Rewrite

y^{2} - y - x - 3 - x^{2} + x + y + 1 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

(y + 2)^{2} - x^{2} + y - 9 = 0

9 x^{2} - y^{2} - 36 x - 6 y + 36 = 0

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

yy = x^{2} - 2 x

36 x^{2} - 64 y^{2} - 504 x + 768 y - 2844 = 0

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