x^2+4y^2=2

Solution

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

(h, k) = (0, 0), a = 2, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = \frac{1}{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 = \frac{1}{2}

x^{2} + 2 y^{2} - 3 x + 4 y + 0.25 = 0

2 x^{2} + y^{2} = 225

\frac{( x - 2 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{7} = 1

\frac{( x + 3 ) ^{2}}{36} + \frac{( y - 1 ) ^{2}}{16} = 1

4 x^{2} + 9 y^{2} = 40

What is x^2+4y^2=2 ?
The solution to x^2+4y^2=2 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=sqrt(1/2)