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

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

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

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

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

Solution steps

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

Rewrite

x^{2} + \frac{y ^{2}}{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 + 8 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{81} = 1

\frac{( x - 12 ) ^{2}}{289} + \frac{( y - 3 ) ^{2}}{64} = 1

3 x^{2} + 6 y^{2} - 4 x + 6 y - 3 = 0

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - 3 ) ^{2}}{9} = 1

\frac{( x - 4 ) ^{2}}{3} + \frac{y ^{2}}{9} = 1

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