What is x^2+y^2+5y=0 ?

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

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x^2+y^2+5y=0

x^{2} + y^{2} + 5 y = 0

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

Solution steps

x^{2} + y^{2} + 5 y = 0

Rewrite

x^{2} + y^{2} + 5 y = 0

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}

1 x^{2} + 4 y^{2} + 10 x + 9 y - 10 = 0

x^{2} + \frac{( y - 6 ) ^{2}}{16} = 1

x^{2} + (3 y - 3)^{2} = 4

(x - 5)^{2} + 2 (y - 6)^{2} = 36

9 y^{2} = 144 - 16 x^{2}

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