What is 2y^2=-x^2+4 ?

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

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2y^2=-x^2+4

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

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

Solution steps

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

Rewrite

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

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

16 x^{2} - 64 x + 9 y^{2} + 9 y + 1 = 0

\frac{( x + 5 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{144} = 1

\frac{8 x}{x ^{2} + y ^{2} + 1} = 1

(16 - x^{2} - 9 y^{2}) = - 1

36 x^{2} + 17 y^{2} - 648 x + 238 y + 689 = 0

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