-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}

\frac{( x - 7 ) ^{2}}{81} + \frac{( y ) ^{2}}{9} = 1

4 - x^{2} - 4 y^{2} = 1

x (100 - 3 x) + y (192 - 6 y) = 0

X^{2} + \frac{Y ^{2}}{49} = 1

3 x^{2} + 4 y^{2} + 24 x - 16 y + 52 = 0

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