Given the ellipse 3x2 4y2 6x 16y 7 0 the GeneralForm wr

Given the ellipse 3x^2 + 4y^2 - 6x - 16y + 7 = 0 the General-Form, write it in its standard form

3x^2 + 4y^2 - 6x - 16y +7 =0

Rearranging the terms :

3(x^2 - 2x +1 -1) + 4(y^2 - 4y +4 -4 ) +7 =0

3(x -1)^2 -3 + 4(y -2)^2 -16 +7 =0

3(x-1)^2 +4(y -2)^2 =12

(x-1)^2/4 + (y -2)^2/6 =1

It is as per standard equation : (x -h)^2/a^2 + (y -k)^2/b^2 =1

centre ( h, k) = ( 1, 2)