What is the axis x^2+y^2-y=0 ?

The axis x^2+y^2-y=0 is semi-major axis b= 1/2 , semi-minor axis a= 1/2

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axis x^2+y^2-y=0

axis

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

semi - major axis b = \frac{1}{2}, semi - minor axis a = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

3 x^{2} + y^{2} + 2 x - 6 y = 3

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{16} = 1

\frac{x ^{2}}{16} + (y - 4)^{2} = 1

What is the axis x^2+y^2-y=0 ?
The axis x^2+y^2-y=0 is semi-major axis b= 1/2 , semi-minor axis a= 1/2