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

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

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

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

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

Solution steps

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

Rewrite

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

9 x^{2} = 4 y^{2} - 12

9 y^{2} - 16 x^{2} - 36 y + 32 x - 124 = 0

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

- 25 x^{2} + 100 y^{2} + 10 x - 80 y = - 95

25 x^{2} - 64 (y - 6)^{2} = 1600

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