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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 2, b = 1

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{36} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{45} = 1

\frac{( x - 3 ) ^{2} + y ^{2}}{( x + 3 ) ^{2} + y ^{2}} \geq 4

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

4 x^{2} + 9 y^{2} - 8 x = 32

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