What is 3x^2+3y^2-30y=0 ?

The solution to 3x^2+3y^2-30y=0 is Ellipse with (h,k)=(0,5),a=5,b=5

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3x^2+3y^2-30y=0

3 x^{2} + 3 y^{2} - 30 y = 0

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

Solution steps

3 x^{2} + 3 y^{2} - 30 y = 0

Rewrite

3 x^{2} + 3 y^{2} - 30 y = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x + 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

\frac{( x + 2 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

x^{2} + 4 y^{2} + 4 x + 32 y - 64 = 0

\frac{( x - 2 ) ^{2}}{10} + \frac{( y + 1 ) ^{2}}{25} = 1

36 x^{2} + 16 y^{2} + 144 x - 160 y - 32 = 0

What is 3x^2+3y^2-30y=0 ?
The solution to 3x^2+3y^2-30y=0 is Ellipse with (h,k)=(0,5),a=5,b=5