x^2=2y-y^2

Solution

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

(h, k) = (0, 1), a = 1, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 ^{2}} + \frac{( y - 1 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 1), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 1, a = 1

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