x^2=4-2y^2

Solution

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

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

Solution steps

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

Rewrite

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

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

5 x^{2} + y^{2} + 4 x - 16 = 0

\frac{( x + 3 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{4} = 1

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

\frac{( x + 8 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{81} = 1

\frac{( x - 12 ) ^{2}}{289} + \frac{( y - 3 ) ^{2}}{64} = 1

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