Write the equation in standard form:

Question

given the following equation of the ellipse in general form,

3x^2+y^2-6x+4y+4=0, complete the square to write the equation in standard form.

Answer 1

3x²+y²-6x+4y+4=0

3x²-6x+y²+4y+4=0

3(x²-2x+1-1)+(y²+4y+4)=0

3(x-1)²-3+(y+2)²=0

3(x-1)²+(y+2)²=3  (divide both sides by 3)

(x-1)²/1+(y+2)²/3=1 

This is a canonical form of ellipse equation.