What is 2x^2+3y^2=12 ?

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

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2x^2+3y^2=12

2 x^{2} + 3 y^{2} = 12

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

Solution steps

2 x^{2} + 3 y^{2} = 12

Rewrite

2 x^{2} + 3 y^{2} = 12

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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