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

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

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

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

(h, k) = (3, - 1), a = 23, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, - 1), a = 23, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 1), a = 23, b = 2

2 x^{2} + y^{2} = 50

9 x^{2} + 5 y^{2} + 18 x + 10 y - 31 = 0

x^{2} + 5 y^{2} + 10 y + 4 x - 27 = 0

x^{2} + 4 y^{2} \geq 100

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0

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