What is 3x^2+2y^2-12=0 ?

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

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3x^2+2y^2-12=0

3 x^{2} + 2 y^{2} - 12 = 0

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

Solution steps

3 x^{2} + 2 y^{2} - 12 = 0

Rewrite

3 x^{2} + 2 y^{2} - 12 = 0

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

\frac{y ^{2}}{16} + \frac{x ^{2}}{25} = 1

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

\frac{( x - 2 ) ^{2}}{\frac{2}{3}} + \frac{( y - 1 ) ^{2}}{16} = 1

3 x^{2} + 4 y^{2} - 5 x + 2 y + 1 = 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{121} = 1

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