What is 3x^2+3y^2-36y=0 ?

The solution to 3x^2+3y^2-36y=0 is Ellipse with (h,k)=(0,6),a=6,b=6

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3x^2+3y^2-36y=0

3 x^{2} + 3 y^{2} - 36 y = 0

(h, k) = (0, 6), a = 6, b = 6

Solution steps

3 x^{2} + 3 y^{2} - 36 y = 0

Rewrite

3 x^{2} + 3 y^{2} - 36 y = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{6 ^{2}} + \frac{( y - 6 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 6), a = 6, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 6), b = 6, a = 6

4 x^{2} + 8 y^{2} - 4 x - 24 y - 13 = 0

x^{2} + 16 y^{2} - 2 x - 64 y + 49 = 0

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

\frac{( x - 5 ) ^{2}}{2 ^{2}} + \frac{( y - 3 ) ^{2}}{9} = 1

25 x^{2} + 9 y^{2} + 100 x - 125 = 0

What is 3x^2+3y^2-36y=0 ?
The solution to 3x^2+3y^2-36y=0 is Ellipse with (h,k)=(0,6),a=6,b=6