What is 2z^2-2z+1+y^2=1 ?

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

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2z^2-2z+1+y^2=1

2 z^{2} - 2 z + 1 + y^{2} = 1

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

Solution steps

2 z^{2} - 2 z + 1 + y^{2} = 1

Rewrite

2 z^{2} - 2 z + 1 + y^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, 0), b = \frac{1}{2}, a = \frac{1}{2}

2 x^{2} + y^{2} + 6 x - 2 y - 10 = 0

0 = x^{2} + 2 y^{2} - 4

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

\frac{( y - 3 ) ^{2}}{16} + \frac{( x + 2 ) ^{2}}{9} = 1

7 (x - 2004)^{2} = 23 - y^{2}

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