x^2+y^2=y

Solution

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

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

Solution steps

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

Rewrite

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

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}

\frac{x ^{2}}{6} + \frac{y ^{2}}{4} = 1

9 x^{2} - 18 x + 4 y^{2} + 8 y = 23

x^{2} + 4 y^{2} - 80 y + 396 = 0

25 x^{2} + 144 y^{2} = 900

\frac{( x + 5 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{4} = 1

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