What is x^2+1/2 y^2=1 ?

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

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x^2+1/2 y^2=1

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

(h, k) = (0, 0), a = 1, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 2, a = 1

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

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

\frac{x ^{2}}{9} + \frac{y ^{2}}{20} = 1

\frac{x ^{2} + y ^{2} + 8 y - 16}{x ^{2} + y ^{2} + 8 y + 16} = 9

5 x^{2} - 30 x + 9 y^{2} - 3 y + 36 = 0

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