What is 16-x^2-9y^2>= 0 ?

The solution to 16-x^2-9y^2>= 0 is Ellipse with (h,k)=(0,0),a=4,b= 4/3

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16-x^2-9y^2>= 0

16 - x^{2} - 9 y^{2} \geq 0

(h, k) = (0, 0), a = 4, b = \frac{4}{3}

Solution steps

16 - x^{2} - 9 y^{2} \geq 0

Rewrite

16 - x^{2} - 9 y^{2} \geq 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{4}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = \frac{4}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4, b = \frac{4}{3}

9 x^{2} + 6 y^{2} + 54 x - 36 y + 81 = 0

36 x^{2} + 25 y^{2} - 900 = 0

- 8 x^{2} - 2 y^{2} - 12 = 0

(x - 2)^{2} + \frac{( y + 3 ) ^{2}}{16} = 1

81 x^{2} + 64 y^{2} = 25

What is 16-x^2-9y^2>= 0 ?
The solution to 16-x^2-9y^2>= 0 is Ellipse with (h,k)=(0,0),a=4,b= 4/3