What is 15x^2+15y^2+16y>= 0 ?

The solution to 15x^2+15y^2+16y>= 0 is Ellipse with (h,k)=(0,-8/15),a= 8/15 ,b= 8/15

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15x^2+15y^2+16y>= 0

15 x^{2} + 15 y^{2} + 16 y \geq 0

(h, k) = (0, - \frac{8}{15}), a = \frac{8}{15}, b = \frac{8}{15}

Solution steps

15 x^{2} + 15 y^{2} + 16 y \geq 0

Rewrite

15 x^{2} + 15 y^{2} + 16 y \geq 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{8}{15} ) ^{2}} + \frac{( y - ( - \frac{8}{15} ) ) ^{2}}{( \frac{8}{15} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - \frac{8}{15}), a = \frac{8}{15}, b = \frac{8}{15}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - \frac{8}{15}), b = \frac{8}{15}, a = \frac{8}{15}

\frac{( y - 3 ) ^{2}}{64} + \frac{( x + 5 ) ^{2}}{81} = 1

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

x^{2} + 5 y^{2} = 20

4 x^{2} + 2 y^{2} + 6 x + 8 y + 4 = 0

\frac{1 + b + ia}{1 + b - ia} = b + ia

What is 15x^2+15y^2+16y>= 0 ?
The solution to 15x^2+15y^2+16y>= 0 is Ellipse with (h,k)=(0,-8/15),a= 8/15 ,b= 8/15