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

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

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

y^{2} \leq - 4 x^{2} + 4

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

Solution steps

y^{2} \leq - 4 x^{2} + 4

Rewrite

y^{2} \leq - 4 x^{2} + 4

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

\frac{( x - 4 ) ^{2}}{35} + \frac{( y - 2 ) ^{2}}{39} = 1

16 - 4 x^{2} - y^{2} > 0

\frac{( X - 7 ) ^{2}}{25} + \frac{( Y - 3 ) ^{2}}{16} = 1

12 x - 3 x^{2} + 36 y - 6 y^{2} > 0

16 x^{2} + 25 y^{2} + 64 x - 200 y + 64 = 0

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