What is x^2+y^2-7y=0 ?

The solution to x^2+y^2-7y=0 is Ellipse with (h,k)=(0, 7/2),a= 7/2 ,b= 7/2

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x^2+y^2-7y=0

x^{2} + y^{2} - 7 y = 0

(h, k) = (0, \frac{7}{2}), a = \frac{7}{2}, b = \frac{7}{2}

Solution steps

x^{2} + y^{2} - 7 y = 0

Rewrite

x^{2} + y^{2} - 7 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{7}{2} ) ^{2}} + \frac{( y - \frac{7}{2} ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, \frac{7}{2}), a = \frac{7}{2}, b = \frac{7}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{7}{2}), b = \frac{7}{2}, a = \frac{7}{2}

\frac{x ^{2}}{7} + \frac{y ^{2}}{5} = 1

\frac{( x + 6 ) ^{2}}{100} + \frac{( y - 8 ) ^{2}}{36} = 1

- 7 x^{2} - 9 y^{2} - 63 = 0

\frac{( ( x + 5 ) ^{2} )}{36} + \frac{( ( y - 1 ) ^{2} )}{9} = 1

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

What is x^2+y^2-7y=0 ?
The solution to x^2+y^2-7y=0 is Ellipse with (h,k)=(0, 7/2),a= 7/2 ,b= 7/2