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}

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