2y^2+x^2=1

Solution

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

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

Solution steps

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

Rewrite

2 y^{2} + x^{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}

36 x^{2} + 4 y^{2} - 49 = 0

9 x^{2} + 4 y^{2} + 72 x - 8 y - 176 = 0

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

\frac{( x - 3 ) ^{2}}{12} + \frac{( y + 4 ) ^{2}}{36} = 1

1 - \frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 0

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