What is 3x^2+3y^2-6y=0 ?

The solution to 3x^2+3y^2-6y=0 is Ellipse with (h,k)=(0,1),a=1,b=1

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3x^2+3y^2-6y=0

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

(h, k) = (0, 1), a = 1, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 1), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 1, a = 1

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{25} = 1

4 x^{2} - 16 x + 9 y^{2} + 54 y + 61 = 0

9 x^{2} + 16 y^{2} - 18 x + 64 y = 71

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

\frac{x ^{2}}{\frac{25}{4}} + \frac{( y + \frac{5}{2} ) ^{2}}{\frac{9}{4}} = 1

What is 3x^2+3y^2-6y=0 ?
The solution to 3x^2+3y^2-6y=0 is Ellipse with (h,k)=(0,1),a=1,b=1