What is 2y-x^2-y^2>0 ?

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

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2y-x^2-y^2>0

2 y - x^{2} - y^{2} > 0

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

Solution steps

2 y - x^{2} - y^{2} > 0

Rewrite

2 y - x^{2} - y^{2} > 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

0 = 9 - x^{2} - 9 y^{2}

25 x^{2} + 36 y^{2} = 900

(\frac{2 x ^{2}}{25}) + (\frac{( y - 3 ) ^{2}}{49}) = 1

(x + 2)^{2} - 1 = - 4 (y + 1)^{2}

9 x^{2} + 4 y^{2} - 18 x + 24 y = 0

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