What is x^2+3y^2+6x+6=0 ?

The solution to x^2+3y^2+6x+6=0 is Ellipse with (h,k)=(-3,0),a=sqrt(3),b=1

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x^2+3y^2+6x+6=0

x^{2} + 3 y^{2} + 6 x + 6 = 0

(h, k) = (- 3, 0), a = 3, b = 1

Solution steps

x^{2} + 3 y^{2} + 6 x + 6 = 0

Rewrite

x^{2} + 3 y^{2} + 6 x + 6 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 0), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 0), a = 3, b = 1

(x^{2} + 8 (y + 5)^{2}) = 20

\frac{( x - 4 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{16} = 1

9 x^{2} + 25 y^{2} - 36 x - 189 = 0

9 x^{2} + 25 y^{2} - 18 x - 150 y + 9 = 0

2 x^{2} + 3 y^{2} + 8 x + 9 y - 10 = 0

What is x^2+3y^2+6x+6=0 ?
The solution to x^2+3y^2+6x+6=0 is Ellipse with (h,k)=(-3,0),a=sqrt(3),b=1