What is x^2+y^2=25y ?

The solution to x^2+y^2=25y is Ellipse with (h,k)=(0, 25/2),a= 25/2 ,b= 25/2

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x^2+y^2=25y

x^{2} + y^{2} = 25 y

(h, k) = (0, \frac{25}{2}), a = \frac{25}{2}, b = \frac{25}{2}

Solution steps

x^{2} + y^{2} = 25 y

Rewrite

x^{2} + y^{2} = 25 y

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{25}{2} ) ^{2}} + \frac{( y - \frac{25}{2} ) ^{2}}{( \frac{25}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, \frac{25}{2}), a = \frac{25}{2}, b = \frac{25}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{25}{2}), b = \frac{25}{2}, a = \frac{25}{2}

\frac{\frac{3 x ^{2}}{4}}{12} + (\frac{\frac{4 y}{4}}{12})^{2} = 1

\frac{( X + 7 ) ^{2}}{16} + \frac{( Y - 5 ) ^{2}}{25} = 1

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

(\frac{X - 2}{2})^{2} + (\frac{Y + 3}{4})^{2} = 1

225 x^{2} + 289 y^{2} = 65025

What is x^2+y^2=25y ?
The solution to x^2+y^2=25y is Ellipse with (h,k)=(0, 25/2),a= 25/2 ,b= 25/2