What is x^2+12x+3y^2-12y=-3 ?

The solution to x^2+12x+3y^2-12y=-3 is Ellipse with (h,k)=(-6,2),a=3sqrt(5),b=sqrt(15)

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x^2+12x+3y^2-12y=-3

x^{2} + 12 x + 3 y^{2} - 12 y = - 3

(h, k) = (- 6, 2), a = 35, b = 15

Solution steps

x^{2} + 12 x + 3 y^{2} - 12 y = - 3

Rewrite

x^{2} + 12 x + 3 y^{2} - 12 y = - 3

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{( 3 5 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( 15 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 2), a = 35, b = 15

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, 2), a = 35, b = 15

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

x^{2} + 4 y^{2} = 100

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

4 x^{2} + y^{2} + 6 y + 5 = 0

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

What is x^2+12x+3y^2-12y=-3 ?
The solution to x^2+12x+3y^2-12y=-3 is Ellipse with (h,k)=(-6,2),a=3sqrt(5),b=sqrt(15)