x^2=6y-y^2

Solution

x^{2} = 6 y - y^{2}

(h, k) = (0, 3), a = 3, b = 3

Solution steps

x^{2} = 6 y - y^{2}

Rewrite

x^{2} = 6 y - y^{2}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 3 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 3), a = 3, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 3), b = 3, a = 3

\frac{( x - 81 ) ^{2}}{6 4 ^{2}} + \frac{( y - 64 ) ^{2}}{8 1 ^{2}} = 1

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

x, 2^{2} = h (x)^{2} + (\frac{x}{2})^{2}

4 x^{2} + y^{2} \leq 17

0.5 = 4 x^{2} + y^{2}

What is x^2=6y-y^2 ?
The solution to x^2=6y-y^2 is Ellipse with (h,k)=(0,3),a=3,b=3