What is x^2+y^2+36y=0 ?

The solution to x^2+y^2+36y=0 is Ellipse with (h,k)=(0,-18),a=18,b=18

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x^2+y^2+36y=0

x^{2} + y^{2} + 36 y = 0

(h, k) = (0, - 18), a = 18, b = 18

Solution steps

x^{2} + y^{2} + 36 y = 0

Rewrite

x^{2} + y^{2} + 36 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 8 ^{2}} + \frac{( y - ( - 18 ) ) ^{2}}{1 8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 18), a = 18, b = 18

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 18), b = 18, a = 18

x^{2} + 9 y^{2} - 2 x + 72 y + 136 = 0

36 x^{2} + 25 y^{2} - 50 y - 875 = 0

\frac{( x - 7 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{36} = 1

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

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{26}{16}} = 1

What is x^2+y^2+36y=0 ?
The solution to x^2+y^2+36y=0 is Ellipse with (h,k)=(0,-18),a=18,b=18