x^2+y^2=5y

Solution

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

(h, k) = (0, \frac{5}{2}), a = \frac{5}{2}, b = \frac{5}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{2} ) ^{2}} + \frac{( y - \frac{5}{2} ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, \frac{5}{2}), a = \frac{5}{2}, b = \frac{5}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{5}{2}), b = \frac{5}{2}, a = \frac{5}{2}

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

9 x^{2} + 81 y^{2} - 729 = 0

x^{2} + 4 y^{2} - 4 x - 8 y + 3 = 0

y^{2} = 9 + \frac{- ( 5 x + 4 ) ( 5 x - 6 )}{2}

x^{2} + 4 y^{2} - 6 x + 16 y = - 9

What is x^2+y^2=5y ?
The solution to x^2+y^2=5y is Ellipse with (h,k)=(0, 5/2),a= 5/2 ,b= 5/2