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} \geq 0

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

Solution steps

2 y - x^{2} - y^{2} \geq 0

Rewrite

2 y - x^{2} - y^{2} \geq 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

25 x^{2} + 4 y^{2} - 8 x + 200 y + 304 = 0

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

\frac{x ^{2}}{25} + \frac{( y - 2 ) ^{2}}{4} = 1

y - 3 = - \frac{x}{4 y} (x - 12)

4 x^{2} - 34 y + 13 y^{2} - 36 = 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