What is x^2+3y^2+18y+18=0 ?

The solution to x^2+3y^2+18y+18=0 is Ellipse with (h,k)=(0,-3),a=3,b=sqrt(3)

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x^2+3y^2+18y+18=0

x^{2} + 3 y^{2} + 18 y + 18 = 0

(h, k) = (0, - 3), a = 3, b = 3

Solution steps

x^{2} + 3 y^{2} + 18 y + 18 = 0

Rewrite

x^{2} + 3 y^{2} + 18 y + 18 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 3), a = 3, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - 3), a = 3, b = 3

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{4} = 1

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{25} = 1

\frac{x ^{2}}{81} + \frac{y ^{2}}{36} = 1

x^{2} + 25 y^{2} - 200 y + 375 = 0

\frac{( x + 1 ) ^{2}}{36} + \frac{( y + 3 ) ^{2}}{25} = 1

What is x^2+3y^2+18y+18=0 ?
The solution to x^2+3y^2+18y+18=0 is Ellipse with (h,k)=(0,-3),a=3,b=sqrt(3)