What is x^2+4y^2>= 100 ?

The solution to x^2+4y^2>= 100 is Ellipse with (h,k)=(0,0),a=10,b=5

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x^2+4y^2>= 100

x^{2} + 4 y^{2} \geq 100

(h, k) = (0, 0), a = 10, b = 5

Solution steps

x^{2} + 4 y^{2} \geq 100

Rewrite

x^{2} + 4 y^{2} \geq 100

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 0 ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 10, b = 5

4 x^{2} + 9 y^{2} + 32 x - 18 y + 37 = 0

9 x^{2} + 6 y^{2} + 36 y = 0

\frac{x ^{2}}{a} + \frac{y ^{2}}{b} = 1

3 x^{2} + 2 y^{2} = 4

16 x^{2} + 4 y^{2} = 64

What is x^2+4y^2>= 100 ?
The solution to x^2+4y^2>= 100 is Ellipse with (h,k)=(0,0),a=10,b=5