3x^2+y^2=6

Solution

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

(h, k) = (0, 0), a = 2, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 6, a = 2

0.2 x^{2} + 2 y^{2} + 4 x - 8 y - 12 = 0

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

5 x^{2} + 4 y^{2} = 1

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

x^{2} + 4 y^{2} = e^{1}

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