What is 3x^2+12y^2+6x-24y+6=0 ?

The solution to 3x^2+12y^2+6x-24y+6=0 is Ellipse with (h,k)=(-1,1),a=sqrt(3),b=(sqrt(3))/2

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3x^2+12y^2+6x-24y+6=0

3 x^{2} + 12 y^{2} + 6 x - 24 y + 6 = 0

(h, k) = (- 1, 1), a = 3, b = \frac{3}{2}

Solution steps

3 x^{2} + 12 y^{2} + 6 x - 24 y + 6 = 0

Rewrite

3 x^{2} + 12 y^{2} + 6 x - 24 y + 6 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = 3, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), a = 3, b = \frac{3}{2}

x^{2} + 4 y^{2} + 2 x - 16 y + 13 = 0

x^{2} + 4 y^{2} = 3

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

9 x^{2} + 4 y^{2} - 36 x - 8 y + 4 = 0

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

What is 3x^2+12y^2+6x-24y+6=0 ?
The solution to 3x^2+12y^2+6x-24y+6=0 is Ellipse with (h,k)=(-1,1),a=sqrt(3),b=(sqrt(3))/2