2x^2+y^2=1

Solution

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

12 x^{2} + 4 y^{2} - 24 x - 4 y + 1 = 0

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{9} = 1

4 x^{2} + 5 y^{2} = 20

\frac{( x - 2 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{81} = 1

36 x^{2} + 16 y^{2} - 180 x + 96 y - 207 = 0

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