3x^2+y^2=4

Solution

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

(h, k) = (0, 0), a = \frac{2}{3}, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2}{3}, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 2, a = \frac{2}{3}

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 0 ) ^{2}}{9} = 1

15 x^{2} + 16 y^{2} = 240

4 y^{2} + 9 x^{2} = 36

2 x^{2} + 3 y^{2} + 12 x = 10

\frac{( x - 2 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{9} = 1

What is 3x^2+y^2=4 ?
The solution to 3x^2+y^2=4 is Ellipse with (h,k)=(0,0),a= 2/(sqrt(3)),b=2