What is 3x^2+2y^2-12x+12y+29=0 ?

The solution to 3x^2+2y^2-12x+12y+29=0 is Ellipse with (h,k)=(2,-3),a=sqrt(1/3),b=sqrt(1/2)

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3x^2+2y^2-12x+12y+29=0

3 x^{2} + 2 y^{2} - 12 x + 12 y + 29 = 0

(h, k) = (2, - 3), a = \frac{1}{3}, b = \frac{1}{2}

Solution steps

3 x^{2} + 2 y^{2} - 12 x + 12 y + 29 = 0

Rewrite

3 x^{2} + 2 y^{2} - 12 x + 12 y + 29 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 3), a = \frac{1}{3}, b = \frac{1}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), b = \frac{1}{2}, a = \frac{1}{3}

\frac{( x - 1 ) ^{2}}{9} + \frac{y ^{2}}{5} = 100

4 x^{2} + 9 y^{2} - 16 x - 18 y - 11 = 0

x^{2} + 3 y^{2} + 2 x - 12 y + 10 = 0

4 x^{2} + 8 y^{2} + 6 x + 10 y - 12 = 0

4 x^{2} + 9 y^{2} - 32 x - 36 y + 64 = 0

What is 3x^2+2y^2-12x+12y+29=0 ?
The solution to 3x^2+2y^2-12x+12y+29=0 is Ellipse with (h,k)=(2,-3),a=sqrt(1/3),b=sqrt(1/2)