x^2+y^2=3y

Solution

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

(h, k) = (0, \frac{3}{2}), a = \frac{3}{2}, b = \frac{3}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, \frac{3}{2}), a = \frac{3}{2}, b = \frac{3}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{3}{2}), b = \frac{3}{2}, a = \frac{3}{2}

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

\frac{( x + 7 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1

\frac{( x - 1 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{9} = 1

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