What is 4-4x^2-y^2>= 0 ?

The solution to 4-4x^2-y^2>= 0 is Ellipse with (h,k)=(0,0),a=1,b=2

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4-4x^2-y^2>= 0

4 - 4 x^{2} - y^{2} \geq 0

(h, k) = (0, 0), a = 1, b = 2

Solution steps

4 - 4 x^{2} - y^{2} \geq 0

Rewrite

4 - 4 x^{2} - y^{2} \geq 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

What is 4-4x^2-y^2>= 0 ?
The solution to 4-4x^2-y^2>= 0 is Ellipse with (h,k)=(0,0),a=1,b=2