Equation of parabola,
3x2+4y2−12x−8y+4=0
(3x2−12x)+(4y2−8y)+4=0
⇒3(x2−4x)+4(y2−2y)+4=0
⇒3(x2−4x+4−4)+4(y2−2y+1−1)+4=0
⇒3(x−2)2−12+4(y−1)2−4+4=0
3(x−2)2+4(y−1)2=12
⇒3(x−2)212+4(y−1)212=1
⇒(x−2)24+(y−1)23=1
Comparing with X2a2+Y2b2=1
X=x−2,Y=y−1,a=2,b=√3,here a>b
Eccentricity : b2=a2(1−e2)
⇒3=4(1−e2)
⇒1−e2=34
⇒e2=1−34=14
⇒e=12
Latus rectum: 2b2a=2×32=3
Coordinated of focus coordinates of focus of eliipse will be (±ae,0)
X=±ae
⇒x−2=±2×12=±1
⇒x=2±1
⇒x=3,1
y=0
⇒y−1=0⇒y=1
Thus coordinate of focus are (3,1) and (1,1)