x^2+y^2=9y

Solution

x^{2} + y^{2} = 9 y

(h, k) = (0, \frac{9}{2}), a = \frac{9}{2}, b = \frac{9}{2}

Solution steps

x^{2} + y^{2} = 9 y

Rewrite

x^{2} + y^{2} = 9 y

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{9}{2} ) ^{2}} + \frac{( y - \frac{9}{2} ) ^{2}}{( \frac{9}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, \frac{9}{2}), a = \frac{9}{2}, b = \frac{9}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{9}{2}), b = \frac{9}{2}, a = \frac{9}{2}

\frac{x ^{2}}{36} + \frac{y ^{2}}{2. 5 ^{2}} = 1

x^{2} + y^{2} = 3 y

2 x^{2} + 5 y^{2} = 10

x^{2} + 36 y^{2} - 16 x - 72 y + 64 = 0

x^{2} + 9 y^{2} + 8 x - 36 y + 43 = 0

What is x^2+y^2=9y ?
The solution to x^2+y^2=9y is Ellipse with (h,k)=(0, 9/2),a= 9/2 ,b= 9/2