x^2+2y^2=1

Solution

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

y^{2} + 2 x^{2} - 2 y + 4 x - 6 = 0

x^{2} + 3 y^{2} - 6 x + 6 y = 0

2 x^{2} + y^{2} = 50

9 x^{2} + 5 y^{2} + 18 x + 10 y - 31 = 0

x^{2} + 5 y^{2} + 10 y + 4 x - 27 = 0

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