y^2+2x^2=4

Solution

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

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

Solution steps

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

Rewrite

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

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

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

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

\frac{( x + 3 ) ^{2}}{6 ^{2}} + \frac{( y + 7 ) ^{2}}{2 ^{2}} = 1

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