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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

2 x^{2} + 10 y^{2} - 12 x - 20 y + 8 = 0

9 x^{2} + y^{2} = 1

4 - 9 x^{2} - 2 y^{2} = 0

9 x^{2} + y^{2} + 18 x + 4 y + 4 = 0

4 x^{2} + y^{2} - 16 x - 6 y + 21 = 0

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