2x^2+y^2=6

Solution

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

(h, k) = (0, 0), a = 3, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, 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 = 3

16 (x - 1)^{2} + 25 (y - 2)^{2} = 400

\frac{( x + 2 ) ^{2}}{9} + \frac{y ^{2}}{16} = 1

(\frac{( x - 2 ) ^{2}}{16}) + (\frac{y ^{2}}{9}) = 1

\frac{x}{x ^{2} + y ^{2}} = \frac{3}{2}

4 x^{2} + 25 y^{2} - 50 y - 75 = 0

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