y^2+2x^2=1

Solution

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

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

Solution steps

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

Rewrite

y^{2} + 2 x^{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}

\frac{( y + 3 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1

y^{2} - 10 y - 12 x + 37 = 0

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

f (x) = x^{2} - 2 x

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

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