x^2+2y^2=6

Solution

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 6, b = 3

9 x^{2} + y^{2} + 144 x = - 567

x^{2} + 4 y^{2} + 2 x - 12 y + 6 = 0

\frac{( x - 6 ) ^{2}}{9} + \frac{( y + 7 ) ^{2}}{25} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

\frac{( x ^{2} )}{4} + y^{2} \frac{1}{9} = 1

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