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}

25 x^{2} + 9 y^{2} - 150 x - 36 y + 36 = 0

100 y^{2} + 64 x^{2} = 6400

(x - 4)^{2} + \frac{( y - 2 ) ^{2}}{9} = 1

4 = \frac{1}{x ^{2} + y ^{2} - 7}

6.25 x^{2} + 16 y^{2} - 1.25 x + 64 y - 29.75 = 0

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