What is 3x^2+3y^2+48y=0 ?

The solution to 3x^2+3y^2+48y=0 is Ellipse with (h,k)=(0,-8),a=8,b=8

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3x^2+3y^2+48y=0

3 x^{2} + 3 y^{2} + 48 y = 0

(h, k) = (0, - 8), a = 8, b = 8

Solution steps

3 x^{2} + 3 y^{2} + 48 y = 0

Rewrite

3 x^{2} + 3 y^{2} + 48 y = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, - 8), a = 8, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 8), b = 8, a = 8

25 x^{(2)} + 4 y^{(2)} = 99

3 x^{2} - 9 x + 2 y^{2} + 10 y - 6 = 0

x^{2} + y^{2} = 10 - x^{2} - 2 y^{2}

- \frac{x ^{2}}{9} - y^{2} = 1

5 x^{2} + 72 y^{2} - 2 > 0

What is 3x^2+3y^2+48y=0 ?
The solution to 3x^2+3y^2+48y=0 is Ellipse with (h,k)=(0,-8),a=8,b=8