2x^2+y^2=4

Solution

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

x^{2} + 10 x + 9 y^{2} + 16 = 0

\frac{( x - 3 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{4} = 1

\frac{x ^{2}}{7 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

3 x^{2} + 7 y^{2} - 12 x - 28 y + 19 = 0

16 x^{2} + 25 y^{2} = 1600

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