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}

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