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

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

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

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

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

Solution steps

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

Rewrite

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

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

(\frac{x + 1}{2})^{2} + (\frac{y - 1}{4})^{2} = \frac{5}{16}

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

\frac{x ^{2}}{625} + \frac{y ^{2}}{400} = 1

14 x^{2} + 8 y^{2} = 112

9 y^{2} + z^{2} = 36

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