y^2=1-2x^2

Solution

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

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

Solution steps

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

Rewrite

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

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}

x^{2} + 2 z^{2} + 6 x - 8 z + 1 = 0

9 x^{2} + 5 y^{2} - 18 x - 20 y - 151 = 0

\frac{x ^{2}}{4} + \frac{( y - 5 ) ^{2}}{5} = 1

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

5 x^{2} + 3 y^{2} - 12 = 0

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