3x^2+4y^2-6x+16y-15=0 find the elipse

Question

How to find the elipse with the equation in general form

Answer 1

3x^2+4y^2-6x+16y-15=0

3(x^2-2x)+4(y^2+4y)-15=0

Complete the squares: 3(x^2-2x+1)+4(y^2+4y+4)-3-16-15=0

3(x-1)^2+4(y+2)^2=34 centre of ellipse is (1,-2)

The equation of the ellipse in standard form is: 3(x-1)^2/34+2(y+2)^2/17=1

Semi-major axis, a=√(34/3), semi-minor axis, b=√(17/2), c=focus=√(17/6), eccentricity, e=c/a=1/2.