What is x^2=(4-y^2)/2 ?

The solution to x^2=(4-y^2)/2 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2

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x^2=(4-y^2)/2

x^{2} = \frac{4 - y ^{2}}{2}

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

Solution steps

x^{2} = \frac{4 - y ^{2}}{2}

Rewrite

x^{2} - \frac{4 - y ^{2}}{2} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

64 x^{2} - 192 x - 156 + 100 y^{2} - 200 y = 0

\frac{( x - 3 ) ^{2}}{64} + \frac{( y + 4 ) ^{2}}{81} = 1

49 x^{2} + 4 y^{2} + 98 x - 147 = 0

9 x^{2} + 25 y^{2} - 144 x + 200 y + 751 = 0

\frac{4 x ^{2}}{19} + \frac{2 y ^{2}}{19} = 1

What is x^2=(4-y^2)/2 ?
The solution to x^2=(4-y^2)/2 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2