What is y^2=4+z^2-2z ?

The solution to y^2=4+z^2-2z is Hyperbola with (h,k)=(0,1),a=sqrt(3),b=sqrt(3)

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y^2=4+z^2-2z

y^{2} = 4 + z^{2} - 2 z

(h, k) = (0, 1), a = 3, b = 3

Solution steps

y^{2} = 4 + z^{2} - 2 z

Rewrite

y^{2} = 4 + z^{2} - 2 z

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( 3 ) ^{2}} - \frac{( z - 1 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 1), a = 3, b = 3

a^{2} - b^{2} = 51

10 y^{2} - 9 x^{2} = 144

10 x^{2} - 7 y^{2} - 30 x + 14 y = 5

25 x^{2} - 9 y^{2} + 100 x - 54 y + 10 = 0

y^{2} = x^{2} + 8

What is y^2=4+z^2-2z ?
The solution to y^2=4+z^2-2z is Hyperbola with (h,k)=(0,1),a=sqrt(3),b=sqrt(3)