x^2+y^2=6y

Solution

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

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

Solution steps

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

Rewrite

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

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 + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{169} = 1

25 x^{2} + 4 y^{2} + 50 x - 16 y = 59

16 y^{2} + 25 x^{2} - 80 x + 36 y + 80 = 0

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0

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