-y=x^2+y^2

Solution

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

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

Solution steps

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

Rewrite

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

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