What is 3y^2+x^2-12y+9=0 ?

The solution to 3y^2+x^2-12y+9=0 is Ellipse with (h,k)=(0,2),a=sqrt(3),b=1

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3y^2+x^2-12y+9=0

3 y^{2} + x^{2} - 12 y + 9 = 0

(h, k) = (0, 2), a = 3, b = 1

Solution steps

3 y^{2} + x^{2} - 12 y + 9 = 0

Rewrite

3 y^{2} + x^{2} - 12 y + 9 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - 2 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 2), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 2), a = 3, b = 1

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

16 x^{2} + 4 y^{2} + 16 x + 49 y - 81 = 0

\frac{( x - 4 ) ^{2}}{10} + \frac{( y - 2 ) ^{2}}{6} = 1

9 x^{2} - 18 x + 4 y^{2} - 27 = 0

4 x^{2} + 25 y^{2} + 8 x = 96

What is 3y^2+x^2-12y+9=0 ?
The solution to 3y^2+x^2-12y+9=0 is Ellipse with (h,k)=(0,2),a=sqrt(3),b=1